SOLUTION: solve for x: {{{ 4x^2 - 3x = -12 }}}

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Question 591696: solve for x: +4x%5E2+-+3x+=+-12+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-3x=-12 Start with the given equation.


4x%5E2-3x%2B12=0 Get every term to the left side.


Notice that the quadratic 4x%5E2-3x%2B12 is in the form of Ax%5E2%2BBx%2BC where A=4, B=-3, and C=12


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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%284%29%2812%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-3, and C=12


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%284%29%2812%29+%29%29%2F%282%284%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%284%29%2812%29+%29%29%2F%282%284%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9-192+%29%29%2F%282%284%29%29 Multiply 4%284%29%2812%29 to get 192


x+=+%283+%2B-+sqrt%28+-183+%29%29%2F%282%284%29%29 Subtract 192 from 9 to get -183


x+=+%283+%2B-+sqrt%28+-183+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%283+%2B-+i%2Asqrt%28183%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%283%2Bi%2Asqrt%28183%29%29%2F%288%29 or x+=+%283-i%2Asqrt%28183%29%29%2F%288%29 Break up the expression.


So the solutions are x+=+%283%2Bi%2Asqrt%28183%29%29%2F%288%29 or x+=+%283-i%2Asqrt%28183%29%29%2F%288%29