SOLUTION: Solve. x^2 + 8x + 15 = 0

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Question 88264: Solve. x^2 + 8x + 15 = 0

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Now let's use the quadratic formula to solve for x:


Starting with the general quadratic

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

the general form of 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%2B15=0 (notice a=1, b=8, and c=15)

x+=+%28-8+%2B-+sqrt%28+%288%29%5E2-4%2A1%2A15+%29%29%2F%282%2A1%29 Plug in a=1, b=8, and c=15



x+=+%28-8+%2B-+sqrt%28+64-4%2A1%2A15+%29%29%2F%282%2A1%29 Square 8 to get 64



x+=+%28-8+%2B-+sqrt%28+64%2B-60+%29%29%2F%282%2A1%29 Multiply -4%2A15%2A1 to get -60



x+=+%28-8+%2B-+sqrt%28+4+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



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



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

So now the expression breaks down into two parts

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

Lets look at the first part:

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=-10%2F2 Subtract the terms in the numerator
x=-5 Divide

So another answer is
x=-5

So our solutions are:
x=-3 or x=-5

Notice when we graph x%5E2%2B8%2Ax%2B15 we get:

+graph%28+500%2C+500%2C+-15%2C+7%2C+-15%2C+7%2C1%2Ax%5E2%2B8%2Ax%2B15%29+

and we can see that the roots are x=-3 and x=-5. This verifies our answer