SOLUTION: x^2+12x+4=0 Solve for X

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Question 561072: x^2+12x+4=0
Solve for X
Answer by jim_thompson5910(35256) About Me  (Show Source):
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x%5E2%2B12x%2B4=0 Start with the given equation.


Notice that the quadratic x%5E2%2B12x%2B4 is in the form of Ax%5E2%2BBx%2BC where A=1, B=12, and C=4


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-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29 Plug in A=1, B=12, and C=4


x+=+%28-12+%2B-+sqrt%28+144-4%281%29%284%29+%29%29%2F%282%281%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144-16+%29%29%2F%282%281%29%29 Multiply 4%281%29%284%29 to get 16


x+=+%28-12+%2B-+sqrt%28+128+%29%29%2F%282%281%29%29 Subtract 16 from 144 to get 128


x+=+%28-12+%2B-+sqrt%28+128+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-12+%2B-+8%2Asqrt%282%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-12%29%2F%282%29+%2B-+%288%2Asqrt%282%29%29%2F%282%29 Break up the fraction.


x+=+-6+%2B-+4%2Asqrt%282%29 Reduce.


x+=+-6%2B4%2Asqrt%282%29 or x+=+-6-4%2Asqrt%282%29 Break up the expression.


So the solutions are x+=+-6%2B4%2Asqrt%282%29 or x+=+-6-4%2Asqrt%282%29
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