SOLUTION: 9x^2 = 12x - 2

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Question 227578: 9x^2 = 12x - 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

9x%5E2=12x-2 Start with the given equation.


9x%5E2-12x%2B2=0 Get every term to the left side.


Notice that the quadratic 9x%5E2-12x%2B2 is in the form of Ax%5E2%2BBx%2BC where A=9, B=-12, and C=2


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%289%29%282%29+%29%29%2F%282%289%29%29 Plug in A=9, B=-12, and C=2


x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%289%29%282%29+%29%29%2F%282%289%29%29 Negate -12 to get 12.


x+=+%2812+%2B-+sqrt%28+144-4%289%29%282%29+%29%29%2F%282%289%29%29 Square -12 to get 144.


x+=+%2812+%2B-+sqrt%28+144-72+%29%29%2F%282%289%29%29 Multiply 4%289%29%282%29 to get 72


x+=+%2812+%2B-+sqrt%28+72+%29%29%2F%282%289%29%29 Subtract 72 from 144 to get 72


x+=+%2812+%2B-+sqrt%28+72+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


x+=+%2812+%2B-+6%2Asqrt%282%29%29%2F%2818%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%2812%2B6%2Asqrt%282%29%29%2F%2818%29 or x+=+%2812-6%2Asqrt%282%29%29%2F%2818%29 Break up the expression.


x+=+%282%2Bsqrt%282%29%29%2F%283%29 or x+=+%282-sqrt%282%29%29%2F%283%29 Reduce.


So the solutions are x+=+%282%2Bsqrt%282%29%29%2F%283%29 or x+=+%282-sqrt%282%29%29%2F%283%29


which approximate to x=1.138 or x=0.195