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Simplifying 16x3 + -10x2 + 14x = 0 Reorder the terms: 14x + -10x2 + 16x3 = 0 Solving 14x + -10x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(7 + -5x + 8x2) = 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 '(7 + -5x + 8x2)' equal to zero and attempt to solve: Simplifying 7 + -5x + 8x2 = 0 Solving 7 + -5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + -0.625x + x2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -0.625x + -0.875 + x2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -0.625x + x2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -0.625x + x2 = 0 + -0.875 -0.625x + x2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -0.625x + x2 = -0.875 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = -0.875 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = -0.875 + 0.09765625 Combine like terms: -0.875 + 0.09765625 = -0.77734375 0.09765625 + -0.625x + x2 = -0.77734375 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = -0.77734375 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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