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Simplifying 10x3 + 16x2 + 14x = 0 Reorder the terms: 14x + 16x2 + 10x3 = 0 Solving 14x + 16x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(7 + 8x + 5x2) = 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 + 8x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + 8x + 5x2 = 0 Solving 7 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 1.6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 1.6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 1.6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 1.6x + x2 = 0 + -1.4 1.6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 1.6x + x2 = -1.4 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = -1.4 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = -1.4 + 0.64 Combine like terms: -1.4 + 0.64 = -0.76 0.64 + 1.6x + x2 = -0.76 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = -0.76 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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