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Simplifying 4x(3x2 + -4x + 5) = 0 Reorder the terms: 4x(5 + -4x + 3x2) = 0 (5 * 4x + -4x * 4x + 3x2 * 4x) = 0 (20x + -16x2 + 12x3) = 0 Solving 20x + -16x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(5 + -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 '(5 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + -4x + 3x2 = 0 Solving 5 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1.333333333x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1.333333333x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + -1.666666667 -1.333333333x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1.333333333x + x2 = -1.666666667 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 = -1.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -1.666666667 + 0.4444444442 Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228 0.4444444442 + -1.333333333x + x2 = -1.2222222228 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -1.2222222228 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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