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Simplifying 2x + 12x * x + -8x = x * x * x Multiply x * x 2x + 12x2 + -8x = x * x * x Reorder the terms: 2x + -8x + 12x2 = x * x * x Combine like terms: 2x + -8x = -6x -6x + 12x2 = x * x * x Multiply x * x -6x + 12x2 = x2 * x Multiply x2 * x -6x + 12x2 = x3 Solving -6x + 12x2 = x3 Solving for variable 'x'. Combine like terms: x3 + -1x3 = 0 -6x + 12x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 12x + -1x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-6 + 12x + -1x2)' equal to zero and attempt to solve: Simplifying -6 + 12x + -1x2 = 0 Solving -6 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -12x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -12x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -12x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -12x + x2 = 0 + -6 -12x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -12x + x2 = -6 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -6 + 36 Reorder the terms: 36 + -12x + x2 = -6 + 36 Combine like terms: -6 + 36 = 30 36 + -12x + x2 = 30 Factor a perfect square on the left side: (x + -6)(x + -6) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + -6) equal to 5.477225575 and -5.477225575.Subproblem 1
x + -6 = 5.477225575 Simplifying x + -6 = 5.477225575 Reorder the terms: -6 + x = 5.477225575 Solving -6 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.477225575 + 6 x = 5.477225575 + 6 Combine like terms: 5.477225575 + 6 = 11.477225575 x = 11.477225575 Simplifying x = 11.477225575Subproblem 2
x + -6 = -5.477225575 Simplifying x + -6 = -5.477225575 Reorder the terms: -6 + x = -5.477225575 Solving -6 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.477225575 + 6 x = -5.477225575 + 6 Combine like terms: -5.477225575 + 6 = 0.522774425 x = 0.522774425 Simplifying x = 0.522774425Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.477225575, 0.522774425}Solution
x = {0, 11.477225575, 0.522774425}
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