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Simplifying (8x3 + 4x2) + -1(5x2 + -12x) = 0 Reorder the terms: (4x2 + 8x3) + -1(5x2 + -12x) = 0 Remove parenthesis around (4x2 + 8x3) 4x2 + 8x3 + -1(5x2 + -12x) = 0 Reorder the terms: 4x2 + 8x3 + -1(-12x + 5x2) = 0 4x2 + 8x3 + (-12x * -1 + 5x2 * -1) = 0 4x2 + 8x3 + (12x + -5x2) = 0 Reorder the terms: 12x + 4x2 + -5x2 + 8x3 = 0 Combine like terms: 4x2 + -5x2 = -1x2 12x + -1x2 + 8x3 = 0 Solving 12x + -1x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(12 + -1x + 8x2) = 0Subproblem 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 '(12 + -1x + 8x2)' equal to zero and attempt to solve: Simplifying 12 + -1x + 8x2 = 0 Solving 12 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.5 + -0.125x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.125x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.125x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.125x + x2 = 0 + -1.5 -0.125x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.125x + x2 = -1.5 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = -1.5 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = -1.5 + 0.00390625 Combine like terms: -1.5 + 0.00390625 = -1.49609375 0.00390625 + -0.125x + x2 = -1.49609375 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = -1.49609375 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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