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Simplifying 8x5 + 4x4 + 12x3 = 0 Reorder the terms: 12x3 + 4x4 + 8x5 = 0 Solving 12x3 + 4x4 + 8x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x3'. 4x3(3 + x + 2x2) = 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 + x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + x + 2x2 = 0 Solving 3 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 0.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 0.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 0.5x + x2 = 0 + -1.5 0.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 0.5x + x2 = -1.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = -1.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -1.5 + 0.25 Combine like terms: -1.5 + 0.25 = -1.25 0.25 + 0.5x + x2 = -1.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.25 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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