SOLUTION: Solve x^2+8x-20=0 Thanks for any help

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Question 89288: Solve
x^2+8x-20=0
Thanks for any help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B8%2Ax-20=0 ( notice a=1, b=8, and c=-20)

x+=+%28-8+%2B-+sqrt%28+%288%29%5E2-4%2A1%2A-20+%29%29%2F%282%2A1%29 Plug in a=1, b=8, and c=-20



x+=+%28-8+%2B-+sqrt%28+64-4%2A1%2A-20+%29%29%2F%282%2A1%29 Square 8 to get 64



x+=+%28-8+%2B-+sqrt%28+64%2B80+%29%29%2F%282%2A1%29 Multiply -4%2A-20%2A1 to get 80



x+=+%28-8+%2B-+sqrt%28+144+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-8+%2B-+12%29%2F%282%2A1%29 Simplify the square root



x+=+%28-8+%2B-+12%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-8+%2B+12%29%2F2 or x+=+%28-8+-+12%29%2F2

Lets look at the first part:

x=%28-8+%2B+12%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=%28-8+-+12%29%2F2

x=-20%2F2 Subtract the terms in the numerator
x=-10 Divide

So another answer is
x=-10

So our solutions are:
x=2 or x=-10

Notice when we graph x%5E2%2B8%2Ax-20, we get:

+graph%28+500%2C+500%2C+-20%2C+12%2C+-20%2C+12%2C1%2Ax%5E2%2B8%2Ax%2B-20%29+

and we can see that the roots are x=2 and x=-10. This verifies our answer