SOLUTION: Solve. x^2 + 6x – 27 = 0

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Question 104968: Solve. x^2 + 6x – 27 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
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%2B6%2Ax-27=0 ( notice a=1, b=6, and c=-27)





x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A1%2A-27+%29%29%2F%282%2A1%29 Plug in a=1, b=6, and c=-27




x+=+%28-6+%2B-+sqrt%28+36-4%2A1%2A-27+%29%29%2F%282%2A1%29 Square 6 to get 36




x+=+%28-6+%2B-+sqrt%28+36%2B108+%29%29%2F%282%2A1%29 Multiply -4%2A-27%2A1 to get 108




x+=+%28-6+%2B-+sqrt%28+144+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-6+%2B-+12%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-6+%2B-+12%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-6+%2B+12%29%2F2 or x+=+%28-6+-+12%29%2F2


Lets look at the first part:


x=%28-6+%2B+12%29%2F2


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=%28-6+-+12%29%2F2


x=-18%2F2 Subtract the terms in the numerator

x=-9 Divide


So another answer is

x=-9


So our solutions are:

x=3 or x=-9