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Simplifying 6x3 + 5x2 + 120x = 0 Reorder the terms: 120x + 5x2 + 6x3 = 0 Solving 120x + 5x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(120 + 5x + 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 '(120 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying 120 + 5x + 6x2 = 0 Solving 120 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 20 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + 0.8333333333x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 0.8333333333x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 0.8333333333x + x2 = 0 + -20 0.8333333333x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 0.8333333333x + x2 = -20 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = -20 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = -20 + 0.1736111111 Combine like terms: -20 + 0.1736111111 = -19.8263888889 0.1736111111 + 0.8333333333x + x2 = -19.8263888889 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = -19.8263888889 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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