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Simplifying x2 + 125x + -180 = 0 Reorder the terms: -180 + 125x + x2 = 0 Solving -180 + 125x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 125x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 125x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 125x + x2 = 0 + 180 125x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 125x + x2 = 180 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 = 180 + 3906.25 Reorder the terms: 3906.25 + 125x + x2 = 180 + 3906.25 Combine like terms: 180 + 3906.25 = 4086.25 3906.25 + 125x + x2 = 4086.25 Factor a perfect square on the left side: (x + 62.5)(x + 62.5) = 4086.25 Calculate the square root of the right side: 63.923782742 Break this problem into two subproblems by setting (x + 62.5) equal to 63.923782742 and -63.923782742.Subproblem 1
x + 62.5 = 63.923782742 Simplifying x + 62.5 = 63.923782742 Reorder the terms: 62.5 + x = 63.923782742 Solving 62.5 + x = 63.923782742 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 = 63.923782742 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + x = 63.923782742 + -62.5 x = 63.923782742 + -62.5 Combine like terms: 63.923782742 + -62.5 = 1.423782742 x = 1.423782742 Simplifying x = 1.423782742Subproblem 2
x + 62.5 = -63.923782742 Simplifying x + 62.5 = -63.923782742 Reorder the terms: 62.5 + x = -63.923782742 Solving 62.5 + x = -63.923782742 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 = -63.923782742 + -62.5 Combine like terms: 62.5 + -62.5 = 0.0 0.0 + x = -63.923782742 + -62.5 x = -63.923782742 + -62.5 Combine like terms: -63.923782742 + -62.5 = -126.423782742 x = -126.423782742 Simplifying x = -126.423782742Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.423782742, -126.423782742}
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