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Simplifying 12x2 + -128x + -374 = 0 Reorder the terms: -374 + -128x + 12x2 = 0 Solving -374 + -128x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-187 + -64x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-187 + -64x + 6x2)' equal to zero and attempt to solve: Simplifying -187 + -64x + 6x2 = 0 Solving -187 + -64x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -31.16666667 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '31.16666667' to each side of the equation. -31.16666667 + -10.66666667x + 31.16666667 + x2 = 0 + 31.16666667 Reorder the terms: -31.16666667 + 31.16666667 + -10.66666667x + x2 = 0 + 31.16666667 Combine like terms: -31.16666667 + 31.16666667 = 0.00000000 0.00000000 + -10.66666667x + x2 = 0 + 31.16666667 -10.66666667x + x2 = 0 + 31.16666667 Combine like terms: 0 + 31.16666667 = 31.16666667 -10.66666667x + x2 = 31.16666667 The x term is -10.66666667x. Take half its coefficient (-5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. -10.66666667x + 28.44444446 + x2 = 31.16666667 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = 31.16666667 + 28.44444446 Combine like terms: 31.16666667 + 28.44444446 = 59.61111113 28.44444446 + -10.66666667x + x2 = 59.61111113 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 59.61111113 Calculate the square root of the right side: 7.720823216 Break this problem into two subproblems by setting (x + -5.333333335) equal to 7.720823216 and -7.720823216.Subproblem 1
x + -5.333333335 = 7.720823216 Simplifying x + -5.333333335 = 7.720823216 Reorder the terms: -5.333333335 + x = 7.720823216 Solving -5.333333335 + x = 7.720823216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = 7.720823216 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 7.720823216 + 5.333333335 x = 7.720823216 + 5.333333335 Combine like terms: 7.720823216 + 5.333333335 = 13.054156551 x = 13.054156551 Simplifying x = 13.054156551Subproblem 2
x + -5.333333335 = -7.720823216 Simplifying x + -5.333333335 = -7.720823216 Reorder the terms: -5.333333335 + x = -7.720823216 Solving -5.333333335 + x = -7.720823216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = -7.720823216 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -7.720823216 + 5.333333335 x = -7.720823216 + 5.333333335 Combine like terms: -7.720823216 + 5.333333335 = -2.387489881 x = -2.387489881 Simplifying x = -2.387489881Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.054156551, -2.387489881}Solution
x = {13.054156551, -2.387489881}
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