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Simplifying -10x6 + 12x5 + -4x4 = 0 Reorder the terms: -4x4 + 12x5 + -10x6 = 0 Solving -4x4 + 12x5 + -10x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x4'. 2x4(-2 + 6x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 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 '(-2 + 6x + -5x2)' equal to zero and attempt to solve: Simplifying -2 + 6x + -5x2 = 0 Solving -2 + 6x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.4 + -1.2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.2x + x2 = 0 + -0.4 -1.2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.2x + x2 = -0.4 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -0.4 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.4 + 0.36 Combine like terms: -0.4 + 0.36 = -0.04 0.36 + -1.2x + x2 = -0.04 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = -0.04 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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