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Simplifying 24x5 + 6x4 + 3x3 = 0 Reorder the terms: 3x3 + 6x4 + 24x5 = 0 Solving 3x3 + 6x4 + 24x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x3'. 3x3(1 + 2x + 8x2) = 0 Ignore the factor 3.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 '(1 + 2x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + 8x2 = 0 Solving 1 + 2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 0.25x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 0.25x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 0.25x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 0.25x + x2 = 0 + -0.125 0.25x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 0.25x + x2 = -0.125 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = -0.125 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = -0.125 + 0.015625 Combine like terms: -0.125 + 0.015625 = -0.109375 0.015625 + 0.25x + x2 = -0.109375 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = -0.109375 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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