SOLUTION: how would you solve for 8x squared – 12x = 11

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Question 189008: how would you solve for 8x squared – 12x = 11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8x%5E2-12x=11 Start with the given equation.


8x%5E2-12x-11=0 Subtract 11 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=8, b=-12, and c=-11


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-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%288%29%28-11%29+%29%29%2F%282%288%29%29 Plug in a=8, b=-12, and c=-11


x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%288%29%28-11%29+%29%29%2F%282%288%29%29 Negate -12 to get 12.


x+=+%2812+%2B-+sqrt%28+144-4%288%29%28-11%29+%29%29%2F%282%288%29%29 Square -12 to get 144.


x+=+%2812+%2B-+sqrt%28+144--352+%29%29%2F%282%288%29%29 Multiply 4%288%29%28-11%29 to get -352


x+=+%2812+%2B-+sqrt%28+144%2B352+%29%29%2F%282%288%29%29 Rewrite sqrt%28144--352%29 as sqrt%28144%2B352%29


x+=+%2812+%2B-+sqrt%28+496+%29%29%2F%282%288%29%29 Add 144 to 352 to get 496


x+=+%2812+%2B-+sqrt%28+496+%29%29%2F%2816%29 Multiply 2 and 8 to get 16.


x+=+%2812+%2B-+4%2Asqrt%2831%29%29%2F%2816%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%2812%2B4%2Asqrt%2831%29%29%2F%2816%29 or x+=+%2812-4%2Asqrt%2831%29%29%2F%2816%29 Break up the expression.


x+=+%283%2Bsqrt%2831%29%29%2F%284%29 or x+=+%283-sqrt%2831%29%29%2F%284%29 Reduce


So the answers are x+=+%283%2Bsqrt%2831%29%29%2F%284%29 or x+=+%283-sqrt%2831%29%29%2F%284%29