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Simplifying 4x4 + -6x3 + 48x2 = 0 Reorder the terms: 48x2 + -6x3 + 4x4 = 0 Solving 48x2 + -6x3 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(24 + -3x + 2x2) = 0 Ignore the factor 2.Subproblem 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 '(24 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying 24 + -3x + 2x2 = 0 Solving 24 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12 + -1.5x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -1.5x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -1.5x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1.5x + x2 = 0 + -12 -1.5x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -1.5x + x2 = -12 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -12 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -12 + 0.5625 Combine like terms: -12 + 0.5625 = -11.4375 0.5625 + -1.5x + x2 = -11.4375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -11.4375 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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