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Simplifying 3x4 + -8x3 + 6x2 = 0 Reorder the terms: 6x2 + -8x3 + 3x4 = 0 Solving 6x2 + -8x3 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(6 + -8x + 3x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(6 + -8x + 3x2)' equal to zero and attempt to solve: Simplifying 6 + -8x + 3x2 = 0 Solving 6 + -8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.666666667x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2.666666667x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.666666667x + x2 = 0 + -2 -2.666666667x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.666666667x + x2 = -2 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = -2 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -2 + 1.777777780 Combine like terms: -2 + 1.777777780 = -0.22222222 1.777777780 + -2.666666667x + x2 = -0.22222222 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = -0.22222222 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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