SOLUTION: 8x(6x+7)=-3

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Question 248052: 8x(6x+7)=-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
8x%286x%2B7%29=-3 Start with the given equation.


48x%5E2%2B56x=-3 Distribute


48x%5E2%2B56x%2B3=0 Add 3 to both sides.


Notice that the quadratic 48x%5E2%2B56x%2B3 is in the form of Ax%5E2%2BBx%2BC where A=48, B=56, and C=3


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-%2856%29+%2B-+sqrt%28+%2856%29%5E2-4%2848%29%283%29+%29%29%2F%282%2848%29%29 Plug in A=48, B=56, and C=3


x+=+%28-56+%2B-+sqrt%28+3136-4%2848%29%283%29+%29%29%2F%282%2848%29%29 Square 56 to get 3136.


x+=+%28-56+%2B-+sqrt%28+3136-576+%29%29%2F%282%2848%29%29 Multiply 4%2848%29%283%29 to get 576


x+=+%28-56+%2B-+sqrt%28+2560+%29%29%2F%282%2848%29%29 Subtract 576 from 3136 to get 2560


x+=+%28-56+%2B-+sqrt%28+2560+%29%29%2F%2896%29 Multiply 2 and 48 to get 96.


x+=+%28-56+%2B-+16%2Asqrt%2810%29%29%2F%2896%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-56%2B16%2Asqrt%2810%29%29%2F%2896%29 or x+=+%28-56-16%2Asqrt%2810%29%29%2F%2896%29 Break up the expression.


So the solutions are x+=+%28-56%2B16%2Asqrt%2810%29%29%2F%2896%29 or x+=+%28-56-16%2Asqrt%2810%29%29%2F%2896%29


which approximate to x=-0.056 or x=-1.11