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Simplifying 6x3 + 13x2 + 44x = 0 Reorder the terms: 44x + 13x2 + 6x3 = 0 Solving 44x + 13x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(44 + 13x + 6x2) = 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 '(44 + 13x + 6x2)' equal to zero and attempt to solve: Simplifying 44 + 13x + 6x2 = 0 Solving 44 + 13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 7.333333333 + 2.166666667x + x2 = 0 Move the constant term to the right: Add '-7.333333333' to each side of the equation. 7.333333333 + 2.166666667x + -7.333333333 + x2 = 0 + -7.333333333 Reorder the terms: 7.333333333 + -7.333333333 + 2.166666667x + x2 = 0 + -7.333333333 Combine like terms: 7.333333333 + -7.333333333 = 0.000000000 0.000000000 + 2.166666667x + x2 = 0 + -7.333333333 2.166666667x + x2 = 0 + -7.333333333 Combine like terms: 0 + -7.333333333 = -7.333333333 2.166666667x + x2 = -7.333333333 The x term is 2.166666667x. Take half its coefficient (1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. 2.166666667x + 1.173611113 + x2 = -7.333333333 + 1.173611113 Reorder the terms: 1.173611113 + 2.166666667x + x2 = -7.333333333 + 1.173611113 Combine like terms: -7.333333333 + 1.173611113 = -6.15972222 1.173611113 + 2.166666667x + x2 = -6.15972222 Factor a perfect square on the left side: (x + 1.083333334)(x + 1.083333334) = -6.15972222 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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