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Simplifying 6x3 + -8x2 + 14x = 0 Reorder the terms: 14x + -8x2 + 6x3 = 0 Solving 14x + -8x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(7 + -4x + 3x2) = 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 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + -4x + 3x2 = 0 Solving 7 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -1.333333333x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -1.333333333x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + -2.333333333 -1.333333333x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -1.333333333x + x2 = -2.333333333 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -2.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -2.333333333 + 0.4444444442 Combine like terms: -2.333333333 + 0.4444444442 = -1.8888888888 0.4444444442 + -1.333333333x + x2 = -1.8888888888 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -1.8888888888 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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