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Simplifying 0 = 4x2 + -400x + 24000 Reorder the terms: 0 = 24000 + -400x + 4x2 Solving 0 = 24000 + -400x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -24000 = -24000 -24000 + 400x + -4x2 = 24000 + -400x + 4x2 + -24000 + 400x + -4x2 Reorder the terms: -24000 + 400x + -4x2 = 24000 + -24000 + -400x + 400x + 4x2 + -4x2 Combine like terms: 24000 + -24000 = 0 -24000 + 400x + -4x2 = 0 + -400x + 400x + 4x2 + -4x2 -24000 + 400x + -4x2 = -400x + 400x + 4x2 + -4x2 Combine like terms: -400x + 400x = 0 -24000 + 400x + -4x2 = 0 + 4x2 + -4x2 -24000 + 400x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -24000 + 400x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6000 + 100x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6000 + 100x + -1x2)' equal to zero and attempt to solve: Simplifying -6000 + 100x + -1x2 = 0 Solving -6000 + 100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6000 + -100x + x2 = 0 Move the constant term to the right: Add '-6000' to each side of the equation. 6000 + -100x + -6000 + x2 = 0 + -6000 Reorder the terms: 6000 + -6000 + -100x + x2 = 0 + -6000 Combine like terms: 6000 + -6000 = 0 0 + -100x + x2 = 0 + -6000 -100x + x2 = 0 + -6000 Combine like terms: 0 + -6000 = -6000 -100x + x2 = -6000 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -6000 + 2500 Reorder the terms: 2500 + -100x + x2 = -6000 + 2500 Combine like terms: -6000 + 2500 = -3500 2500 + -100x + x2 = -3500 Factor a perfect square on the left side: (x + -50)(x + -50) = -3500 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. The solution to this equation could not be determined.
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