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Simplifying 2x(6x2 + 8x + -6) = 0 Reorder the terms: 2x(-6 + 8x + 6x2) = 0 (-6 * 2x + 8x * 2x + 6x2 * 2x) = 0 (-12x + 16x2 + 12x3) = 0 Solving -12x + 16x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-3 + 4x + 3x2) = 0 Ignore the factor 4.Subproblem 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 '(-3 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying -3 + 4x + 3x2 = 0 Solving -3 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.333333333x + x2 = 0 + 1 1.333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.333333333x + x2 = 1 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 1 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 1 + 0.4444444442 Combine like terms: 1 + 0.4444444442 = 1.4444444442 0.4444444442 + 1.333333333x + x2 = 1.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.201850425 and -1.201850425.Subproblem 1
x + 0.6666666665 = 1.201850425 Simplifying x + 0.6666666665 = 1.201850425 Reorder the terms: 0.6666666665 + x = 1.201850425 Solving 0.6666666665 + x = 1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.201850425 + -0.6666666665 x = 1.201850425 + -0.6666666665 Combine like terms: 1.201850425 + -0.6666666665 = 0.5351837585 x = 0.5351837585 Simplifying x = 0.5351837585Subproblem 2
x + 0.6666666665 = -1.201850425 Simplifying x + 0.6666666665 = -1.201850425 Reorder the terms: 0.6666666665 + x = -1.201850425 Solving 0.6666666665 + x = -1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.201850425 + -0.6666666665 x = -1.201850425 + -0.6666666665 Combine like terms: -1.201850425 + -0.6666666665 = -1.8685170915 x = -1.8685170915 Simplifying x = -1.8685170915Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5351837585, -1.8685170915}Solution
x = {0, 0.5351837585, -1.8685170915}
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