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Simplifying 0 = -15x3 + 9x2 + -6x Reorder the terms: 0 = -6x + 9x2 + -15x3 Solving 0 = -6x + 9x2 + -15x3 Solving for variable 'x'. Remove the zero: 6x + -9x2 + 15x3 = -6x + 9x2 + -15x3 + 6x + -9x2 + 15x3 Reorder the terms: 6x + -9x2 + 15x3 = -6x + 6x + 9x2 + -9x2 + -15x3 + 15x3 Combine like terms: -6x + 6x = 0 6x + -9x2 + 15x3 = 0 + 9x2 + -9x2 + -15x3 + 15x3 6x + -9x2 + 15x3 = 9x2 + -9x2 + -15x3 + 15x3 Combine like terms: 9x2 + -9x2 = 0 6x + -9x2 + 15x3 = 0 + -15x3 + 15x3 6x + -9x2 + 15x3 = -15x3 + 15x3 Combine like terms: -15x3 + 15x3 = 0 6x + -9x2 + 15x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(2 + -3x + 5x2) = 0 Ignore the factor 3.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 '(2 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + -3x + 5x2 = 0 Solving 2 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -0.6x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -0.6x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -0.6x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.6x + x2 = 0 + -0.4 -0.6x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -0.6x + x2 = -0.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = -0.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = -0.4 + 0.09 Combine like terms: -0.4 + 0.09 = -0.31 0.09 + -0.6x + x2 = -0.31 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = -0.31 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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