SOLUTION: x2+7x+10=0 I guess

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Question 112101: x2+7x+10=0 I guess
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%2B7%2Ax%2B10=0 ( notice a=1, b=7, and c=10)




x+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29 Plug in a=1, b=7, and c=10



x+=+%28-7+%2B-+sqrt%28+49-4%2A1%2A10+%29%29%2F%282%2A1%29 Square 7 to get 49



x+=+%28-7+%2B-+sqrt%28+49%2B-40+%29%29%2F%282%2A1%29 Multiply -4%2A10%2A1 to get -40



x+=+%28-7+%2B-+sqrt%28+9+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-7+%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+=+%28-7+%2B-+3%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-7+%2B+3%29%2F2 or x+=+%28-7+-+3%29%2F2

Lets look at the first part:

x=%28-7+%2B+3%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=%28-7+-+3%29%2F2

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

So another answer is
x=-5

So our solutions are:
x=-2 or x=-5

Notice when we graph x%5E2%2B7%2Ax%2B10, we get:

+graph%28+500%2C+500%2C+-15%2C+8%2C+-15%2C+8%2C1%2Ax%5E2%2B7%2Ax%2B10%29+

and we can see that the roots are x=-2 and x=-5. This verifies our answer