SOLUTION: 6x^2+6x+8=0

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Question 527340: 6x^2+6x+8=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
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6x%5E2%2B6x%2B8=0 Start with the given equation.


Notice that the quadratic 6x%5E2%2B6x%2B8 is in the form of Ax%5E2%2BBx%2BC where A=6, B=6, and C=8


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-%286%29+%2B-+sqrt%28+%286%29%5E2-4%286%29%288%29+%29%29%2F%282%286%29%29 Plug in A=6, B=6, and C=8


x+=+%28-6+%2B-+sqrt%28+36-4%286%29%288%29+%29%29%2F%282%286%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-192+%29%29%2F%282%286%29%29 Multiply 4%286%29%288%29 to get 192


x+=+%28-6+%2B-+sqrt%28+-156+%29%29%2F%282%286%29%29 Subtract 192 from 36 to get -156


x+=+%28-6+%2B-+sqrt%28+-156+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-6+%2B-+2i%2Asqrt%2839%29%29%2F%2812%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%2B2i%2Asqrt%2839%29%29%2F%2812%29 or x+=+%28-6-2i%2Asqrt%2839%29%29%2F%2812%29 Break up the expression.


x+=+%28-3%2Bi%2Asqrt%2839%29%29%2F%286%29 or x+=+%28-3-i%2Asqrt%2839%29%29%2F%286%29 Reduce


So the solutions are x+=+%28-3%2Bi%2Asqrt%2839%29%29%2F%286%29 or x+=+%28-3-i%2Asqrt%2839%29%29%2F%286%29


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Jim