SOLUTION: i have 4 question and i need solutiions too please 1)x^2-1=0 2)x^2-7=0 3)3x^2-12=0 4)5x^2-15=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: i have 4 question and i need solutiions too please 1)x^2-1=0 2)x^2-7=0 3)3x^2-12=0 4)5x^2-15=0      Log On


   

Question 408083: i have 4 question and i need solutiions too please
1)x^2-1=0

2)x^2-7=0

3)3x^2-12=0

4)5x^2-15=0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1)
x%5E2-1=0
x%5E2=1
x=+-sqrt%281%29
x1=1
x2=-1

2)
x%5E2-7=0
x%5E2=7
x=+-sqrt%287%29
x1=2.65
x2=-2.65

3)
3x%5E2-12=0
x%5E2=12
x=+-sqrt%2812%29
x1=3.46
x2=-3.46

4)
5x%5E2-15=0

5x%5E2=15

5x%5E2%2F5=15%2F5

x%5E2=3
x=+-sqrt%283%29
x1=1.73
x2=-1.73


I will add here your questions from 16-25....

16.
16)x^2+2x-3=0.

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2B2%2Ax-3=0 ( notice a=1, b=2, and c=-3)





x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29 Plug in a=1, b=2, and c=-3




x+=+%28-2+%2B-+sqrt%28+4-4%2A1%2A-3+%29%29%2F%282%2A1%29 Square 2 to get 4




x+=+%28-2+%2B-+sqrt%28+4%2B12+%29%29%2F%282%2A1%29 Multiply -4%2A-3%2A1 to get 12




x+=+%28-2+%2B-+sqrt%28+16+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-2+%2B-+4%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-2+%2B-+4%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-2+%2B+4%29%2F2 or x+=+%28-2+-+4%29%2F2


Lets look at the first part:


x=%28-2+%2B+4%29%2F2


x=2%2F2 Add the terms in the numerator

x=1 Divide


So one answer is

x=1




Now lets look at the second part:


x=%28-2+-+4%29%2F2


x=-6%2F2 Subtract the terms in the numerator

x=-3 Divide


So another answer is

x=-3


So our solutions are:

x=1 or x=-3




17)x^2-5x+6=0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-5%2Ax%2B6=0 ( notice a=1, b=-5, and c=6)





x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29 Plug in a=1, b=-5, and c=6




x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29 Negate -5 to get 5




x+=+%285+%2B-+sqrt%28+25-4%2A1%2A6+%29%29%2F%282%2A1%29 Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because %28-5%29%5E2=-5%2A-5=25.)




x+=+%285+%2B-+sqrt%28+25%2B-24+%29%29%2F%282%2A1%29 Multiply -4%2A6%2A1 to get -24




x+=+%285+%2B-+sqrt%28+1+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%285+%2B-+1%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%285+%2B-+1%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%285+%2B+1%29%2F2 or x+=+%285+-+1%29%2F2


Lets look at the first part:


x=%285+%2B+1%29%2F2


x=6%2F2 Add the terms in the numerator

x=3 Divide


So one answer is

x=3




Now lets look at the second part:


x=%285+-+1%29%2F2


x=4%2F2 Subtract the terms in the numerator

x=2 Divide


So another answer is

x=2


So our solutions are:

x=3 or x=2




18)x^2-7x-8=0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-7%2Ax-8=0 ( notice a=1, b=-7, and c=-8)





x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Plug in a=1, b=-7, and c=-8




x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-8+%29%29%2F%282%2A1%29 Negate -7 to get 7




x+=+%287+%2B-+sqrt%28+49-4%2A1%2A-8+%29%29%2F%282%2A1%29 Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because %28-7%29%5E2=-7%2A-7=49.)




x+=+%287+%2B-+sqrt%28+49%2B32+%29%29%2F%282%2A1%29 Multiply -4%2A-8%2A1 to get 32




x+=+%287+%2B-+sqrt%28+81+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%287+%2B-+9%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%287+%2B-+9%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%287+%2B+9%29%2F2 or x+=+%287+-+9%29%2F2


Lets look at the first part:


x=%287+%2B+9%29%2F2


x=16%2F2 Add the terms in the numerator

x=8 Divide


So one answer is

x=8




Now lets look at the second part:


x=%287+-+9%29%2F2


x=-2%2F2 Subtract the terms in the numerator

x=-1 Divide


So another answer is

x=-1


So our solutions are:

x=8 or x=-1




19)x^2+x-20=0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2Bx-20=0 ( notice a=1, b=1, and c=-20)





x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A-20+%29%29%2F%282%2A1%29 Plug in a=1, b=1, and c=-20




x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A-20+%29%29%2F%282%2A1%29 Square 1 to get 1




x+=+%28-1+%2B-+sqrt%28+1%2B80+%29%29%2F%282%2A1%29 Multiply -4%2A-20%2A1 to get 80




x+=+%28-1+%2B-+sqrt%28+81+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-1+%2B-+9%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-1+%2B-+9%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-1+%2B+9%29%2F2 or x+=+%28-1+-+9%29%2F2


Lets look at the first part:


x=%28-1+%2B+9%29%2F2


x=8%2F2 Add the terms in the numerator

x=4 Divide


So one answer is

x=4




Now lets look at the second part:


x=%28-1+-+9%29%2F2


x=-10%2F2 Subtract the terms in the numerator

x=-5 Divide


So another answer is

x=-5


So our solutions are:

x=4 or x=-5



20)6-x-x^2=0..reorder
-x^2 -x +6 =0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve -x%5E2-x%2B6=0 ( notice a=-1, b=-1, and c=6)





x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A-1%2A6+%29%29%2F%282%2A-1%29 Plug in a=-1, b=-1, and c=6




x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A-1%2A6+%29%29%2F%282%2A-1%29 Negate -1 to get 1




x+=+%281+%2B-+sqrt%28+1-4%2A-1%2A6+%29%29%2F%282%2A-1%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)




x+=+%281+%2B-+sqrt%28+1%2B24+%29%29%2F%282%2A-1%29 Multiply -4%2A6%2A-1 to get 24




x+=+%281+%2B-+sqrt%28+25+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)




x+=+%281+%2B-+5%29%2F%282%2A-1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%281+%2B-+5%29%2F-2 Multiply 2 and -1 to get -2


So now the expression breaks down into two parts


x+=+%281+%2B+5%29%2F-2 or x+=+%281+-+5%29%2F-2


Lets look at the first part:


x=%281+%2B+5%29%2F-2


x=6%2F-2 Add the terms in the numerator

x=-3 Divide


So one answer is

x=-3




Now lets look at the second part:


x=%281+-+5%29%2F-2


x=-4%2F-2 Subtract the terms in the numerator

x=2 Divide


So another answer is

x=2


So our solutions are:

x=-3 or x=2




21)4+5x+x^2=0
x^2+5x+4=0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2B5%2Ax%2B4=0 ( notice a=1, b=5, and c=4)





x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29 Plug in a=1, b=5, and c=4




x+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A4+%29%29%2F%282%2A1%29 Square 5 to get 25




x+=+%28-5+%2B-+sqrt%28+25%2B-16+%29%29%2F%282%2A1%29 Multiply -4%2A4%2A1 to get -16




x+=+%28-5+%2B-+sqrt%28+9+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-5+%2B-+3%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-5+%2B-+3%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-5+%2B+3%29%2F2 or x+=+%28-5+-+3%29%2F2


Lets look at the first part:


x=%28-5+%2B+3%29%2F2


x=-2%2F2 Add the terms in the numerator

x=-1 Divide


So one answer is

x=-1




Now lets look at the second part:


x=%28-5+-+3%29%2F2


x=-8%2F2 Subtract the terms in the numerator

x=-4 Divide


So another answer is

x=-4


So our solutions are:

x=-1 or x=-4




22)24+2x-x^2=0
-x^2 +2x + 24=0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve -x%5E2%2B2%2Ax%2B24=0 ( notice a=-1, b=2, and c=24)





x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A-1%2A24+%29%29%2F%282%2A-1%29 Plug in a=-1, b=2, and c=24




x+=+%28-2+%2B-+sqrt%28+4-4%2A-1%2A24+%29%29%2F%282%2A-1%29 Square 2 to get 4




x+=+%28-2+%2B-+sqrt%28+4%2B96+%29%29%2F%282%2A-1%29 Multiply -4%2A24%2A-1 to get 96




x+=+%28-2+%2B-+sqrt%28+100+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-2+%2B-+10%29%2F%282%2A-1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-2+%2B-+10%29%2F-2 Multiply 2 and -1 to get -2


So now the expression breaks down into two parts


x+=+%28-2+%2B+10%29%2F-2 or x+=+%28-2+-+10%29%2F-2


Lets look at the first part:


x=%28-2+%2B+10%29%2F-2


x=8%2F-2 Add the terms in the numerator

x=-4 Divide


So one answer is

x=-4




Now lets look at the second part:


x=%28-2+-+10%29%2F-2


x=-12%2F-2 Subtract the terms in the numerator

x=6 Divide


So another answer is

x=6


So our solutions are:

x=-4 or x=6




23)8x^2-1=0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 8%2Ax%5E2-1=0 (note: since the polynomial does not have an "x" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like 8%2Ax%5E2%2B0%2Ax-1=0 notice a=8, b=0, and c=-1)





x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A8%2A-1+%29%29%2F%282%2A8%29 Plug in a=8, b=0, and c=-1




x+=+%280+%2B-+sqrt%28+0-4%2A8%2A-1+%29%29%2F%282%2A8%29 Square 0 to get 0




x+=+%280+%2B-+sqrt%28+0%2B32+%29%29%2F%282%2A8%29 Multiply -4%2A-1%2A8 to get 32




x+=+%280+%2B-+sqrt%28+32+%29%29%2F%282%2A8%29 Combine like terms in the radicand (everything under the square root)




x+=+%280+%2B-+4%2Asqrt%282%29%29%2F%282%2A8%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%280+%2B-+4%2Asqrt%282%29%29%2F16 Multiply 2 and 8 to get 16


So now the expression breaks down into two parts


x+=+%280+%2B+4%2Asqrt%282%29%29%2F16 or x+=+%280+-+4%2Asqrt%282%29%29%2F16



Now break up the fraction



x=0%2F16%2B4%2Asqrt%282%29%2F16 or x=0%2F16-4%2Asqrt%282%29%2F16



Simplify



x=0%2Bsqrt%282%29%2F4 or x=0-sqrt%282%29%2F4



So the solutions are:

x=0%2Bsqrt%282%29%2F4 or x=0-sqrt%282%29%2F4





24)6x^2+5x+1=0

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 6%2Ax%5E2%2B5%2Ax%2B1=0 ( notice a=6, b=5, and c=1)





x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A6%2A1+%29%29%2F%282%2A6%29 Plug in a=6, b=5, and c=1




x+=+%28-5+%2B-+sqrt%28+25-4%2A6%2A1+%29%29%2F%282%2A6%29 Square 5 to get 25




x+=+%28-5+%2B-+sqrt%28+25%2B-24+%29%29%2F%282%2A6%29 Multiply -4%2A1%2A6 to get -24




x+=+%28-5+%2B-+sqrt%28+1+%29%29%2F%282%2A6%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-5+%2B-+1%29%2F%282%2A6%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-5+%2B-+1%29%2F12 Multiply 2 and 6 to get 12


So now the expression breaks down into two parts


x+=+%28-5+%2B+1%29%2F12 or x+=+%28-5+-+1%29%2F12


Lets look at the first part:


x=%28-5+%2B+1%29%2F12


x=-4%2F12 Add the terms in the numerator

x=-1%2F3 Divide


So one answer is

x=-1%2F3




Now lets look at the second part:


x=%28-5+-+1%29%2F12


x=-6%2F12 Subtract the terms in the numerator

x=-1%2F2 Divide


So another answer is

x=-1%2F2



25)3x^2-5x-28=0
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 3%2Ax%5E2-5%2Ax-28=0 ( notice a=3, b=-5, and c=-28)





x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A-28+%29%29%2F%282%2A3%29 Plug in a=3, b=-5, and c=-28




x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A3%2A-28+%29%29%2F%282%2A3%29 Negate -5 to get 5




x+=+%285+%2B-+sqrt%28+25-4%2A3%2A-28+%29%29%2F%282%2A3%29 Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because %28-5%29%5E2=-5%2A-5=25.)




x+=+%285+%2B-+sqrt%28+25%2B336+%29%29%2F%282%2A3%29 Multiply -4%2A-28%2A3 to get 336




x+=+%285+%2B-+sqrt%28+361+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%285+%2B-+19%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%285+%2B-+19%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%285+%2B+19%29%2F6 or x+=+%285+-+19%29%2F6


Lets look at the first part:


x=%285+%2B+19%29%2F6


x=24%2F6 Add the terms in the numerator

x=4 Divide


So one answer is

x=4




Now lets look at the second part:


x=%285+-+19%29%2F6


x=-14%2F6 Subtract the terms in the numerator

x=-7%2F3 Divide


So another answer is

x=-7%2F3


So our solutions are:

x=4 or x=-7%2F3