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Simplifying -6000x2 + -6000x + -120000 = 0 Reorder the terms: -120000 + -6000x + -6000x2 = 0 Solving -120000 + -6000x + -6000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-6000'. -6000(20 + x + x2) = 0 Ignore the factor -6000.Subproblem 1
Set the factor '(20 + x + x2)' equal to zero and attempt to solve: Simplifying 20 + x + x2 = 0 Solving 20 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + x + x2 = 0 + -20 x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 x + x2 = -20 The x term is x. 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. x + 0.25 + x2 = -20 + 0.25 Reorder the terms: 0.25 + x + x2 = -20 + 0.25 Combine like terms: -20 + 0.25 = -19.75 0.25 + x + x2 = -19.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -19.75 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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