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Simplifying 16x3 + 14x2 + 18x = 0 Reorder the terms: 18x + 14x2 + 16x3 = 0 Solving 18x + 14x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(9 + 7x + 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 '(9 + 7x + 8x2)' equal to zero and attempt to solve: Simplifying 9 + 7x + 8x2 = 0 Solving 9 + 7x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + 0.875x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + 0.875x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + 0.875x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + 0.875x + x2 = 0 + -1.125 0.875x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 0.875x + x2 = -1.125 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = -1.125 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = -1.125 + 0.19140625 Combine like terms: -1.125 + 0.19140625 = -0.93359375 0.19140625 + 0.875x + x2 = -0.93359375 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = -0.93359375 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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