SOLUTION: Can you help me with this equation {{{x^2+12x-64=0}}}

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Question 200196This question is from textbook Mathematics in Our World
: Can you help me with this equation
x%5E2%2B12x-64=0 This question is from textbook Mathematics in Our World

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B12x-64=0 Start with the given equation.


Notice that the quadratic x%5E2%2B12x-64 is in the form of Ax%5E2%2BBx%2BC where A=1, B=12, and C=-64


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%28-64%29+%29%29%2F%282%281%29%29 Plug in A=1, B=12, and C=-64


x+=+%28-12+%2B-+sqrt%28+144-4%281%29%28-64%29+%29%29%2F%282%281%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144--256+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-64%29 to get -256


x+=+%28-12+%2B-+sqrt%28+144%2B256+%29%29%2F%282%281%29%29 Rewrite sqrt%28144--256%29 as sqrt%28144%2B256%29


x+=+%28-12+%2B-+sqrt%28+400+%29%29%2F%282%281%29%29 Add 144 to 256 to get 400


x+=+%28-12+%2B-+sqrt%28+400+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-12+%2B-+20%29%2F%282%29 Take the square root of 400 to get 20.


x+=+%28-12+%2B+20%29%2F%282%29 or x+=+%28-12+-+20%29%2F%282%29 Break up the expression.


x+=+%288%29%2F%282%29 or x+=++%28-32%29%2F%282%29 Combine like terms.


x+=+4 or x+=+-16 Simplify.


So the solutions are x+=+4 or x+=+-16