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Simplifying x2 + -125x = 25 Reorder the terms: -125x + x2 = 25 Solving -125x + x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -125x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -125x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -125x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -125x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -125x + x2 = 0 + 25 -125x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -125x + x2 = 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 = 25 + 3906.25 Reorder the terms: 3906.25 + -125x + x2 = 25 + 3906.25 Combine like terms: 25 + 3906.25 = 3931.25 3906.25 + -125x + x2 = 3931.25 Factor a perfect square on the left side: (x + -62.5)(x + -62.5) = 3931.25 Calculate the square root of the right side: 62.69968102 Break this problem into two subproblems by setting (x + -62.5) equal to 62.69968102 and -62.69968102.Subproblem 1
x + -62.5 = 62.69968102 Simplifying x + -62.5 = 62.69968102 Reorder the terms: -62.5 + x = 62.69968102 Solving -62.5 + x = 62.69968102 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 = 62.69968102 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = 62.69968102 + 62.5 x = 62.69968102 + 62.5 Combine like terms: 62.69968102 + 62.5 = 125.19968102 x = 125.19968102 Simplifying x = 125.19968102Subproblem 2
x + -62.5 = -62.69968102 Simplifying x + -62.5 = -62.69968102 Reorder the terms: -62.5 + x = -62.69968102 Solving -62.5 + x = -62.69968102 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 = -62.69968102 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = -62.69968102 + 62.5 x = -62.69968102 + 62.5 Combine like terms: -62.69968102 + 62.5 = -0.19968102 x = -0.19968102 Simplifying x = -0.19968102Solution
The solution to the problem is based on the solutions from the subproblems. x = {125.19968102, -0.19968102}
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