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Simplifying 250x + -2x2 = 100 Solving 250x + -2x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 250x + -2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 250x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 125x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 125x + -1x2)' equal to zero and attempt to solve: Simplifying -50 + 125x + -1x2 = 0 Solving -50 + 125x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 50 + -125x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -125x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -125x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -125x + x2 = 0 + -50 -125x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -125x + x2 = -50 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 = -50 + 3906.25 Reorder the terms: 3906.25 + -125x + x2 = -50 + 3906.25 Combine like terms: -50 + 3906.25 = 3856.25 3906.25 + -125x + x2 = 3856.25 Factor a perfect square on the left side: (x + -62.5)(x + -62.5) = 3856.25 Calculate the square root of the right side: 62.098711742 Break this problem into two subproblems by setting (x + -62.5) equal to 62.098711742 and -62.098711742.Subproblem 1
x + -62.5 = 62.098711742 Simplifying x + -62.5 = 62.098711742 Reorder the terms: -62.5 + x = 62.098711742 Solving -62.5 + x = 62.098711742 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 = 62.098711742 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = 62.098711742 + 62.5 x = 62.098711742 + 62.5 Combine like terms: 62.098711742 + 62.5 = 124.598711742 x = 124.598711742 Simplifying x = 124.598711742Subproblem 2
x + -62.5 = -62.098711742 Simplifying x + -62.5 = -62.098711742 Reorder the terms: -62.5 + x = -62.098711742 Solving -62.5 + x = -62.098711742 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 = -62.098711742 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = -62.098711742 + 62.5 x = -62.098711742 + 62.5 Combine like terms: -62.098711742 + 62.5 = 0.401288258 x = 0.401288258 Simplifying x = 0.401288258Solution
The solution to the problem is based on the solutions from the subproblems. x = {124.598711742, 0.401288258}Solution
x = {124.598711742, 0.401288258}
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