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Simplifying 2x2 + -250x + 2500 = 0 Reorder the terms: 2500 + -250x + 2x2 = 0 Solving 2500 + -250x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1250 + -125x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1250 + -125x + x2)' equal to zero and attempt to solve: Simplifying 1250 + -125x + x2 = 0 Solving 1250 + -125x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1250' to each side of the equation. 1250 + -125x + -1250 + x2 = 0 + -1250 Reorder the terms: 1250 + -1250 + -125x + x2 = 0 + -1250 Combine like terms: 1250 + -1250 = 0 0 + -125x + x2 = 0 + -1250 -125x + x2 = 0 + -1250 Combine like terms: 0 + -1250 = -1250 -125x + x2 = -1250 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 = -1250 + 3906.25 Reorder the terms: 3906.25 + -125x + x2 = -1250 + 3906.25 Combine like terms: -1250 + 3906.25 = 2656.25 3906.25 + -125x + x2 = 2656.25 Factor a perfect square on the left side: (x + -62.5)(x + -62.5) = 2656.25 Calculate the square root of the right side: 51.53882032 Break this problem into two subproblems by setting (x + -62.5) equal to 51.53882032 and -51.53882032.Subproblem 1
x + -62.5 = 51.53882032 Simplifying x + -62.5 = 51.53882032 Reorder the terms: -62.5 + x = 51.53882032 Solving -62.5 + x = 51.53882032 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 = 51.53882032 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = 51.53882032 + 62.5 x = 51.53882032 + 62.5 Combine like terms: 51.53882032 + 62.5 = 114.03882032 x = 114.03882032 Simplifying x = 114.03882032Subproblem 2
x + -62.5 = -51.53882032 Simplifying x + -62.5 = -51.53882032 Reorder the terms: -62.5 + x = -51.53882032 Solving -62.5 + x = -51.53882032 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 = -51.53882032 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = -51.53882032 + 62.5 x = -51.53882032 + 62.5 Combine like terms: -51.53882032 + 62.5 = 10.96117968 x = 10.96117968 Simplifying x = 10.96117968Solution
The solution to the problem is based on the solutions from the subproblems. x = {114.03882032, 10.96117968}Solution
x = {114.03882032, 10.96117968}
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