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Simplifying 2x(12x2 + 13x + 5) = 0 Reorder the terms: 2x(5 + 13x + 12x2) = 0 (5 * 2x + 13x * 2x + 12x2 * 2x) = 0 (10x + 26x2 + 24x3) = 0 Solving 10x + 26x2 + 24x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(5 + 13x + 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 '(5 + 13x + 12x2)' equal to zero and attempt to solve: Simplifying 5 + 13x + 12x2 = 0 Solving 5 + 13x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + 1.083333333x + x2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + 1.083333333x + -0.4166666667 + x2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + 1.083333333x + x2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + 1.083333333x + x2 = 0 + -0.4166666667 1.083333333x + x2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 1.083333333x + x2 = -0.4166666667 The x term is 1.083333333x. Take half its coefficient (0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. 1.083333333x + 0.2934027776 + x2 = -0.4166666667 + 0.2934027776 Reorder the terms: 0.2934027776 + 1.083333333x + x2 = -0.4166666667 + 0.2934027776 Combine like terms: -0.4166666667 + 0.2934027776 = -0.1232638891 0.2934027776 + 1.083333333x + x2 = -0.1232638891 Factor a perfect square on the left side: (x + 0.5416666665)(x + 0.5416666665) = -0.1232638891 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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