SOLUTION: i need some help with these i am trying to solve these by quadratic equation formula and these are the answer that i came up with. (x - 1)^2 = 7 i am getting 1 +- sqrt 7 x^2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: i need some help with these i am trying to solve these by quadratic equation formula and these are the answer that i came up with. (x - 1)^2 = 7 i am getting 1 +- sqrt 7 x^2      Log On


   

Question 107173: i need some help with these i am trying to solve these by quadratic equation formula and these are the answer that i came up with.
(x - 1)^2 = 7
i am getting 1 +- sqrt 7
x^2 - 9x - 4 = 6
i get -1 and a 10
4x^2 - 8x + 3 = 5
i am getting 2 +-sqrt 6/2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28x+-+1%29%5E2+=+7
x-1+=+sqrt%287%29
x+=+sqrt%287%29+%96+1
x+=+2.64+%2B+1
x+=+3.64
Check:
(3.64 – 1)^2 = 7
2.64)^2 = 7

x^2 - 9x - 4 = 6 …move 6 to the left
x^2 – 9x – 4 – 6 = 0
x^2 – 9x – 10 = 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%5E2-9%2Ax-10=0 ( notice a=1, b=-9, and c=-10)





x+=+%28--9+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A-10+%29%29%2F%282%2A1%29 Plug in a=1, b=-9, and c=-10




x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A-10+%29%29%2F%282%2A1%29 Negate -9 to get 9




x+=+%289+%2B-+sqrt%28+81-4%2A1%2A-10+%29%29%2F%282%2A1%29 Square -9 to get 81 (note: remember when you square -9, you must square the negative as well. This is because %28-9%29%5E2=-9%2A-9=81.)




x+=+%289+%2B-+sqrt%28+81%2B40+%29%29%2F%282%2A1%29 Multiply -4%2A-10%2A1 to get 40




x+=+%289+%2B-+sqrt%28+121+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%289+%2B-+11%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%289+%2B-+11%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%289+%2B+11%29%2F2 or x+=+%289+-+11%29%2F2


Lets look at the first part:


x=%289+%2B+11%29%2F2


x=20%2F2 Add the terms in the numerator

x=10 Divide


So one answer is

x=10




Now lets look at the second part:


x=%289+-+11%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=10 or x=-1





4x%5E2+-+8x+%2B+3+=+5+… move 6 to the left
4x%5E2+%96+8x+%2B+3+%96+5+=+0
+4x%5E2+%96+8x+%96+2+=+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 4%2Ax%5E2-8%2Ax-2=0 ( notice a=4, b=-8, and c=-2)





x+=+%28--8+%2B-+sqrt%28+%28-8%29%5E2-4%2A4%2A-2+%29%29%2F%282%2A4%29 Plug in a=4, b=-8, and c=-2




x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%2A4%2A-2+%29%29%2F%282%2A4%29 Negate -8 to get 8




x+=+%288+%2B-+sqrt%28+64-4%2A4%2A-2+%29%29%2F%282%2A4%29 Square -8 to get 64 (note: remember when you square -8, you must square the negative as well. This is because %28-8%29%5E2=-8%2A-8=64.)




x+=+%288+%2B-+sqrt%28+64%2B32+%29%29%2F%282%2A4%29 Multiply -4%2A-2%2A4 to get 32




x+=+%288+%2B-+sqrt%28+96+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




x+=+%288+%2B-+4%2Asqrt%286%29%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%288+%2B-+4%2Asqrt%286%29%29%2F8 Multiply 2 and 4 to get 8


So now the expression breaks down into two parts


x+=+%288+%2B+4%2Asqrt%286%29%29%2F8 or x+=+%288+-+4%2Asqrt%286%29%29%2F8



Now break up the fraction



x=%2B8%2F8%2B4%2Asqrt%286%29%2F8 or x=%2B8%2F8-4%2Asqrt%286%29%2F8



Simplify



x=1%2Bsqrt%286%29%2F2 or x=1-sqrt%286%29%2F2



So the solutions are:

x=1%2Bsqrt%286%29%2F2 or x=1-sqrt%286%29%2F2