SOLUTION: I am having problems with this one. x^2+2x-8=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I am having problems with this one. x^2+2x-8=0      Log On


   

Question 102533: I am having problems with this one.
x^2+2x-8=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%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.....4,2....2 / 1

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

Notice when we graph x%5E2%2B2%2Ax-8, we get:

+graph%28+500%2C+500%2C+-14%2C+12%2C+-14%2C+12%2C1%2Ax%5E2%2B2%2Ax%2B-8%29+

and we can see that the roots are x=2 and x=-4. This verifies our answer