SOLUTION: Tutor, I am think this is incorrect could you please help me with this problem: Solve by using the quadratic formula 4x^2 - 3x + = 0 (no real number solutions?) and

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Tutor, I am think this is incorrect could you please help me with this problem: Solve by using the quadratic formula 4x^2 - 3x + = 0 (no real number solutions?) and       Log On


   

Question 105072: Tutor,
I am think this is incorrect could you please help me with this problem:
Solve by using the quadratic formula
4x^2 - 3x + = 0 (no real number solutions?)
and
X^2 + x - 2 = 0 (is this 1,2 ?)
Any help is appreciated.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Something seems like it's missing...

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%5E2-3%2Ax%2B0=0 (note: since the polynomial does not have a constant term, the 3rd coefficient is zero. In other words, c=0. So that means the polynomial really looks like 4%2Ax%5E2-3%2Ax%2B0=0 notice a=4, b=-3, and c=0)





x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A0+%29%29%2F%282%2A4%29 Plug in a=4, b=-3, and c=0




x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A0+%29%29%2F%282%2A4%29 Negate -3 to get 3




x+=+%283+%2B-+sqrt%28+9-4%2A4%2A0+%29%29%2F%282%2A4%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)




x+=+%283+%2B-+sqrt%28+9%2B0+%29%29%2F%282%2A4%29 Multiply -4%2A0%2A4 to get 0




x+=+%283+%2B-+sqrt%28+9+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




x+=+%283+%2B-+3%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%283+%2B-+3%29%2F8 Multiply 2 and 4 to get 8


So now the expression breaks down into two parts


x+=+%283+%2B+3%29%2F8 or x+=+%283+-+3%29%2F8


Lets look at the first part:


x=%283+%2B+3%29%2F8


x=6%2F8 Add the terms in the numerator

x=3%2F4 Divide


So one answer is

x=3%2F4




Now lets look at the second part:


x=%283+-+3%29%2F8


x=0%2F8 Subtract the terms in the numerator

x=0 Divide


So another answer is

x=0


So our solutions are:

x=3%2F4 or x=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-2=0 ( notice a=1, b=1, and c=-2)





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




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




x+=+%28-1+%2B-+sqrt%28+1%2B8+%29%29%2F%282%2A1%29 Multiply -4%2A-2%2A1 to get 8




x+=+%28-1+%2B-+sqrt%28+9+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




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


So now the expression breaks down into two parts


x+=+%28-1+%2B+3%29%2F2 or x+=+%28-1+-+3%29%2F2


Lets look at the first part:


x=%28-1+%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=%28-1+-+3%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=1 or x=-2