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Simplifying 12x3 + -16x4 + 20x5 = 0 Solving 12x3 + -16x4 + 20x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x3'. 4x3(3 + -4x + 5x2) = 0 Ignore the factor 4.Subproblem 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 '(3 + -4x + 5x2)' equal to zero and attempt to solve: Simplifying 3 + -4x + 5x2 = 0 Solving 3 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -0.8x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -0.8x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -0.8x + x2 = 0 + -0.6 -0.8x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -0.8x + x2 = -0.6 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.6 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.6 + 0.16 Combine like terms: -0.6 + 0.16 = -0.44 0.16 + -0.8x + x2 = -0.44 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = -0.44 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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