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Simplifying x2 + -125x + 20 = 0 Reorder the terms: 20 + -125x + x2 = 0 Solving 20 + -125x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -125x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -125x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -125x + x2 = 0 + -20 -125x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -125x + x2 = -20 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 = -20 + 3906.25 Reorder the terms: 3906.25 + -125x + x2 = -20 + 3906.25 Combine like terms: -20 + 3906.25 = 3886.25 3906.25 + -125x + x2 = 3886.25 Factor a perfect square on the left side: (x + -62.5)(x + -62.5) = 3886.25 Calculate the square root of the right side: 62.339794674 Break this problem into two subproblems by setting (x + -62.5) equal to 62.339794674 and -62.339794674.Subproblem 1
x + -62.5 = 62.339794674 Simplifying x + -62.5 = 62.339794674 Reorder the terms: -62.5 + x = 62.339794674 Solving -62.5 + x = 62.339794674 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 = 62.339794674 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = 62.339794674 + 62.5 x = 62.339794674 + 62.5 Combine like terms: 62.339794674 + 62.5 = 124.839794674 x = 124.839794674 Simplifying x = 124.839794674Subproblem 2
x + -62.5 = -62.339794674 Simplifying x + -62.5 = -62.339794674 Reorder the terms: -62.5 + x = -62.339794674 Solving -62.5 + x = -62.339794674 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 = -62.339794674 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x = -62.339794674 + 62.5 x = -62.339794674 + 62.5 Combine like terms: -62.339794674 + 62.5 = 0.160205326 x = 0.160205326 Simplifying x = 0.160205326Solution
The solution to the problem is based on the solutions from the subproblems. x = {124.839794674, 0.160205326}
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