SOLUTION: Solve by using the quadratic formula. x^2 + 5x – 14 = 0

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Question 125908: Solve by using the quadratic formula. x^2 + 5x – 14 = 0
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%2B5%2Ax-14=0 ( notice a=1, b=5, and c=-14)




x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A-14+%29%29%2F%282%2A1%29 Plug in a=1, b=5, and c=-14



x+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A-14+%29%29%2F%282%2A1%29 Square 5 to get 25



x+=+%28-5+%2B-+sqrt%28+25%2B56+%29%29%2F%282%2A1%29 Multiply -4%2A-14%2A1 to get 56



x+=+%28-5+%2B-+sqrt%28+81+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-5+%2B-+9%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-5+%2B-+9%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-5+%2B+9%29%2F2 or x+=+%28-5+-+9%29%2F2

Lets look at the first part:

x=%28-5+%2B+9%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=%28-5+-+9%29%2F2

x=-14%2F2 Subtract the terms in the numerator
x=-7 Divide

So another answer is
x=-7

So our solutions are:
x=2 or x=-7

Notice when we graph x%5E2%2B5%2Ax-14, we get:

+graph%28+500%2C+500%2C+-17%2C+12%2C+-17%2C+12%2C1%2Ax%5E2%2B5%2Ax%2B-14%29+

and we can see that the roots are x=2 and x=-7. This verifies our answer