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Simplifying 250x + -2x2 = 7812.5 Solving 250x + -2x2 = 7812.5 Solving for variable 'x'. Reorder the terms: -7812.5 + 250x + -2x2 = 7812.5 + -7812.5 Combine like terms: 7812.5 + -7812.5 = 0.0 -7812.5 + 250x + -2x2 = 0.0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3906.25 + -125x + x2 = 0.0 Move the constant term to the right: Add '-3906.25' to each side of the equation. 3906.25 + -125x + -3906.25 + x2 = 0.0 + -3906.25 Reorder the terms: 3906.25 + -3906.25 + -125x + x2 = 0.0 + -3906.25 Combine like terms: 3906.25 + -3906.25 = 0.00 0.00 + -125x + x2 = 0.0 + -3906.25 -125x + x2 = 0.0 + -3906.25 Combine like terms: 0.0 + -3906.25 = -3906.25 -125x + x2 = -3906.25 The x term is -125x. Take half its coefficient (-62.5). Square it (3906.25) and add it to both sides. Add '3906.25' to each side of the equation. -125x + 3906.25 + x2 = -3906.25 + 3906.25 Reorder the terms: 3906.25 + -125x + x2 = -3906.25 + 3906.25 Combine like terms: -3906.25 + 3906.25 = 0.00 3906.25 + -125x + x2 = 0.00 Factor a perfect square on the left side: (x + -62.5)(x + -62.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -62.5) equal to 0.00 and 0.00.Subproblem 1
x + -62.5 = 0.00 Simplifying x + -62.5 = 0.00 Reorder the terms: -62.5 + x = 0.00 Solving -62.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '62.5' to each side of the equation. -62.5 + 62.5 + x = 0.00 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = 0.00 + 62.5 x = 0.00 + 62.5 Combine like terms: 0.00 + 62.5 = 62.5 x = 62.5 Simplifying x = 62.5Subproblem 2
x + -62.5 = 0.00 Simplifying x + -62.5 = 0.00 Reorder the terms: -62.5 + x = 0.00 Solving -62.5 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '62.5' to each side of the equation. -62.5 + 62.5 + x = 0.00 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = 0.00 + 62.5 x = 0.00 + 62.5 Combine like terms: 0.00 + 62.5 = 62.5 x = 62.5 Simplifying x = 62.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.5, 62.5}
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