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Simplifying -12x3 + 480x2 + -6000x = 0 Reorder the terms: -6000x + 480x2 + -12x3 = 0 Solving -6000x + 480x2 + -12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12x'. 12x(-500 + 40x + -1x2) = 0 Ignore the factor 12.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 '(-500 + 40x + -1x2)' equal to zero and attempt to solve: Simplifying -500 + 40x + -1x2 = 0 Solving -500 + 40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 500 + -40x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -40x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -40x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -40x + x2 = 0 + -500 -40x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -40x + x2 = -500 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -500 + 400 Reorder the terms: 400 + -40x + x2 = -500 + 400 Combine like terms: -500 + 400 = -100 400 + -40x + x2 = -100 Factor a perfect square on the left side: (x + -20)(x + -20) = -100 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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