SOLUTION: Use the quadratic formula to solve the equation. x^2 + 2x - 8 = 0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Use the quadratic formula to solve the equation. x^2 + 2x - 8 = 0      Log On


   

Question 102394: Use the quadratic formula to solve the equation.
x^2 + 2x - 8 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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-8=0 ( notice a=1, b=2, and c=-8)





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




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




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




x+=+%28-2+%2B-+sqrt%28+36+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-2+%2B-+6%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-+6%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-2+%2B+6%29%2F2 or x+=+%28-2+-+6%29%2F2


Lets look at the first part:


x=%28-2+%2B+6%29%2F2


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

x=2 Divide


So one answer is

x=2




Now lets look at the second part:


x=%28-2+-+6%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=2 or x=-4