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Simplifying (90 + x)(2500 + -50x) + -1(200000 + -2500x) + -43750 = 0 Multiply (90 + x) * (2500 + -50x) (90(2500 + -50x) + x(2500 + -50x)) + -1(200000 + -2500x) + -43750 = 0 ((2500 * 90 + -50x * 90) + x(2500 + -50x)) + -1(200000 + -2500x) + -43750 = 0 ((225000 + -4500x) + x(2500 + -50x)) + -1(200000 + -2500x) + -43750 = 0 (225000 + -4500x + (2500 * x + -50x * x)) + -1(200000 + -2500x) + -43750 = 0 (225000 + -4500x + (2500x + -50x2)) + -1(200000 + -2500x) + -43750 = 0 Combine like terms: -4500x + 2500x = -2000x (225000 + -2000x + -50x2) + -1(200000 + -2500x) + -43750 = 0 225000 + -2000x + -50x2 + (200000 * -1 + -2500x * -1) + -43750 = 0 225000 + -2000x + -50x2 + (-200000 + 2500x) + -43750 = 0 Reorder the terms: 225000 + -200000 + -43750 + -2000x + 2500x + -50x2 = 0 Combine like terms: 225000 + -200000 = 25000 25000 + -43750 + -2000x + 2500x + -50x2 = 0 Combine like terms: 25000 + -43750 = -18750 -18750 + -2000x + 2500x + -50x2 = 0 Combine like terms: -2000x + 2500x = 500x -18750 + 500x + -50x2 = 0 Solving -18750 + 500x + -50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '50'. 50(-375 + 10x + -1x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-375 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying -375 + 10x + -1x2 = 0 Solving -375 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 375 + -10x + x2 = 0 Move the constant term to the right: Add '-375' to each side of the equation. 375 + -10x + -375 + x2 = 0 + -375 Reorder the terms: 375 + -375 + -10x + x2 = 0 + -375 Combine like terms: 375 + -375 = 0 0 + -10x + x2 = 0 + -375 -10x + x2 = 0 + -375 Combine like terms: 0 + -375 = -375 -10x + x2 = -375 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -375 + 25 Reorder the terms: 25 + -10x + x2 = -375 + 25 Combine like terms: -375 + 25 = -350 25 + -10x + x2 = -350 Factor a perfect square on the left side: (x + -5)(x + -5) = -350 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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