SOLUTION: I need exact solutions for x^2+12x+36=64 I know 2 is one solution, is there another one?

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Question 146762: I need exact solutions for x^2+12x+36=64
I know 2 is one solution, is there another one?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B12x%2B36=64 Start with the given equation.


x%5E2%2B12x%2B36-64=0 Get all terms to the left side.


x%5E2%2B12x-28=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=12, and c=-28


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Plug in a=1, b=12, and c=-28


x+=+%28-12+%2B-+sqrt%28+144-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144--112+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-28%29 to get -112


x+=+%28-12+%2B-+sqrt%28+144%2B112+%29%29%2F%282%281%29%29 Rewrite sqrt%28144--112%29 as sqrt%28144%2B112%29


x+=+%28-12+%2B-+sqrt%28+256+%29%29%2F%282%281%29%29 Add 144 to 112 to get 256


x+=+%28-12+%2B-+sqrt%28+256+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-12+%2B-+16%29%2F%282%29 Take the square root of 256 to get 16.


x+=+%28-12+%2B+16%29%2F%282%29 or x+=+%28-12+-+16%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29 or x+=++%28-28%29%2F%282%29 Combine like terms.


x+=+2 or x+=+-14 Simplify.


So our answers are x+=+2 or x+=+-14