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Simplifying 1000 = x(30 + -2x) 1000 = (30 * x + -2x * x) 1000 = (30x + -2x2) Solving 1000 = 30x + -2x2 Solving for variable 'x'. Reorder the terms: 1000 + -30x + 2x2 = 30x + -30x + -2x2 + 2x2 Combine like terms: 30x + -30x = 0 1000 + -30x + 2x2 = 0 + -2x2 + 2x2 1000 + -30x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 1000 + -30x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(500 + -15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(500 + -15x + x2)' equal to zero and attempt to solve: Simplifying 500 + -15x + x2 = 0 Solving 500 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + -15x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -15x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -15x + x2 = 0 + -500 -15x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -15x + x2 = -500 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -500 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -500 + 56.25 Combine like terms: -500 + 56.25 = -443.75 56.25 + -15x + x2 = -443.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = -443.75 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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