SOLUTION: find the roots of the polynomial equation. x^2 + x - 72 = 0

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Question 292541: find the roots of the polynomial equation. x^2 + x - 72 = 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%2Bx-72=0 ( notice a=1, b=1, and c=-72)





x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A-72+%29%29%2F%282%2A1%29 Plug in a=1, b=1, and c=-72




x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A-72+%29%29%2F%282%2A1%29 Square 1 to get 1




x+=+%28-1+%2B-+sqrt%28+1%2B288+%29%29%2F%282%2A1%29 Multiply -4%2A-72%2A1 to get 288




x+=+%28-1+%2B-+sqrt%28+289+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-1+%2B-+17%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-1+%2B-+17%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-1+%2B+17%29%2F2 or x+=+%28-1+-+17%29%2F2


Lets look at the first part:


x=%28-1+%2B+17%29%2F2


x=16%2F2 Add the terms in the numerator

x=8 Divide


So one answer is

x=8




Now lets look at the second part:


x=%28-1+-+17%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=8 or x=-9