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Simplifying 24x3 = 10x2 + -4x Reorder the terms: 24x3 = -4x + 10x2 Solving 24x3 = -4x + 10x2 Solving for variable 'x'. Reorder the terms: 4x + -10x2 + 24x3 = -4x + 10x2 + 4x + -10x2 Reorder the terms: 4x + -10x2 + 24x3 = -4x + 4x + 10x2 + -10x2 Combine like terms: -4x + 4x = 0 4x + -10x2 + 24x3 = 0 + 10x2 + -10x2 4x + -10x2 + 24x3 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 4x + -10x2 + 24x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(2 + -5x + 12x2) = 0 Ignore the factor 2.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 '(2 + -5x + 12x2)' equal to zero and attempt to solve: Simplifying 2 + -5x + 12x2 = 0 Solving 2 + -5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.1666666667 + -0.4166666667x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.4166666667x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -0.4166666667x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -0.4166666667x + x2 = 0 + -0.1666666667 -0.4166666667x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -0.4166666667x + x2 = -0.1666666667 The x term is -0.4166666667x. Take half its coefficient (-0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. -0.4166666667x + 0.04340277781 + x2 = -0.1666666667 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667x + x2 = -0.1666666667 + 0.04340277781 Combine like terms: -0.1666666667 + 0.04340277781 = -0.12326388889 0.04340277781 + -0.4166666667x + x2 = -0.12326388889 Factor a perfect square on the left side: (x + -0.2083333334)(x + -0.2083333334) = -0.12326388889 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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