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Simplifying 48x3 + -40x2 + 32x = 0 Reorder the terms: 32x + -40x2 + 48x3 = 0 Solving 32x + -40x2 + 48x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x'. 8x(4 + -5x + 6x2) = 0 Ignore the factor 8.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 '(4 + -5x + 6x2)' equal to zero and attempt to solve: Simplifying 4 + -5x + 6x2 = 0 Solving 4 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.8333333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.8333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.8333333333x + x2 = 0 + -0.6666666667 -0.8333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.8333333333x + x2 = -0.6666666667 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = -0.6666666667 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = -0.6666666667 + 0.1736111111 Combine like terms: -0.6666666667 + 0.1736111111 = -0.4930555556 0.1736111111 + -0.8333333333x + x2 = -0.4930555556 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = -0.4930555556 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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