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Simplifying 8x3 + 12x2 + 10x = 0 Reorder the terms: 10x + 12x2 + 8x3 = 0 Solving 10x + 12x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(5 + 6x + 4x2) = 0 Ignore the factor 2.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 '(5 + 6x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 6x + 4x2 = 0 Solving 5 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 1.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 1.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 1.5x + x2 = 0 + -1.25 1.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 1.5x + x2 = -1.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -1.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -1.25 + 0.5625 Combine like terms: -1.25 + 0.5625 = -0.6875 0.5625 + 1.5x + x2 = -0.6875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -0.6875 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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