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Simplifying 2000 = -10000 + 500x + -500x2 Solving 2000 = -10000 + 500x + -500x2 Solving for variable 'x'. Combine like terms: 2000 + 10000 = 12000 12000 + -500x + 500x2 = -10000 + 500x + -500x2 + 10000 + -500x + 500x2 Reorder the terms: 12000 + -500x + 500x2 = -10000 + 10000 + 500x + -500x + -500x2 + 500x2 Combine like terms: -10000 + 10000 = 0 12000 + -500x + 500x2 = 0 + 500x + -500x + -500x2 + 500x2 12000 + -500x + 500x2 = 500x + -500x + -500x2 + 500x2 Combine like terms: 500x + -500x = 0 12000 + -500x + 500x2 = 0 + -500x2 + 500x2 12000 + -500x + 500x2 = -500x2 + 500x2 Combine like terms: -500x2 + 500x2 = 0 12000 + -500x + 500x2 = 0 Factor out the Greatest Common Factor (GCF), '500'. 500(24 + -1x + x2) = 0 Ignore the factor 500.Subproblem 1
Set the factor '(24 + -1x + x2)' equal to zero and attempt to solve: Simplifying 24 + -1x + x2 = 0 Solving 24 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -1x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -1x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1x + x2 = 0 + -24 -1x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -1x + x2 = -24 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -24 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -24 + 0.25 Combine like terms: -24 + 0.25 = -23.75 0.25 + -1x + x2 = -23.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -23.75 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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