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Simplifying 13x3 + 12x2 + 5x = 0 Reorder the terms: 5x + 12x2 + 13x3 = 0 Solving 5x + 12x2 + 13x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 12x + 13x2) = 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 '(5 + 12x + 13x2)' equal to zero and attempt to solve: Simplifying 5 + 12x + 13x2 = 0 Solving 5 + 12x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.3846153846 + 0.9230769231x + x2 = 0 Move the constant term to the right: Add '-0.3846153846' to each side of the equation. 0.3846153846 + 0.9230769231x + -0.3846153846 + x2 = 0 + -0.3846153846 Reorder the terms: 0.3846153846 + -0.3846153846 + 0.9230769231x + x2 = 0 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + 0.9230769231x + x2 = 0 + -0.3846153846 0.9230769231x + x2 = 0 + -0.3846153846 Combine like terms: 0 + -0.3846153846 = -0.3846153846 0.9230769231x + x2 = -0.3846153846 The x term is 0.9230769231x. Take half its coefficient (0.4615384616). Square it (0.2130177515) and add it to both sides. Add '0.2130177515' to each side of the equation. 0.9230769231x + 0.2130177515 + x2 = -0.3846153846 + 0.2130177515 Reorder the terms: 0.2130177515 + 0.9230769231x + x2 = -0.3846153846 + 0.2130177515 Combine like terms: -0.3846153846 + 0.2130177515 = -0.1715976331 0.2130177515 + 0.9230769231x + x2 = -0.1715976331 Factor a perfect square on the left side: (x + 0.4615384616)(x + 0.4615384616) = -0.1715976331 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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