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Simplifying 6x5 + -5x4 + 12x3 = 0 Reorder the terms: 12x3 + -5x4 + 6x5 = 0 Solving 12x3 + -5x4 + 6x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(12 + -5x + 6x2) = 0Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(12 + -5x + 6x2)' equal to zero and attempt to solve: Simplifying 12 + -5x + 6x2 = 0 Solving 12 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.8333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -0.8333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.8333333333x + x2 = 0 + -2 -0.8333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.8333333333x + x2 = -2 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 = -2 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = -2 + 0.1736111111 Combine like terms: -2 + 0.1736111111 = -1.8263888889 0.1736111111 + -0.8333333333x + x2 = -1.8263888889 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = -1.8263888889 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. The solution to this equation could not be determined.
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