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Simplifying 10x3 + -14x2 + 12x = 0 Reorder the terms: 12x + -14x2 + 10x3 = 0 Solving 12x + -14x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(6 + -7x + 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 '(6 + -7x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + -7x + 5x2 = 0 Solving 6 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -1.4x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -1.4x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -1.4x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -1.4x + x2 = 0 + -1.2 -1.4x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -1.4x + x2 = -1.2 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = -1.2 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -1.2 + 0.49 Combine like terms: -1.2 + 0.49 = -0.71 0.49 + -1.4x + x2 = -0.71 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = -0.71 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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