SOLUTION: Give exact and approximate solutions to three decimal places. X^2+12X+36=64

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Question 395439: Give exact and approximate solutions to three decimal places.
X^2+12X+36=64
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 Subtract 64 from both sides.


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


Notice that the quadratic x%5E2%2B12x-28 is 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 the solutions are x+=+2 or x+=+-14

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Jim