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Simplifying x2 + -25x + 140 = 0 Reorder the terms: 140 + -25x + x2 = 0 Solving 140 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-140' to each side of the equation. 140 + -25x + -140 + x2 = 0 + -140 Reorder the terms: 140 + -140 + -25x + x2 = 0 + -140 Combine like terms: 140 + -140 = 0 0 + -25x + x2 = 0 + -140 -25x + x2 = 0 + -140 Combine like terms: 0 + -140 = -140 -25x + x2 = -140 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -140 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -140 + 156.25 Combine like terms: -140 + 156.25 = 16.25 156.25 + -25x + x2 = 16.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -12.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -12.5 = 4.031128874 Simplifying x + -12.5 = 4.031128874 Reorder the terms: -12.5 + x = 4.031128874 Solving -12.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 4.031128874 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 4.031128874 + 12.5 x = 4.031128874 + 12.5 Combine like terms: 4.031128874 + 12.5 = 16.531128874 x = 16.531128874 Simplifying x = 16.531128874Subproblem 2
x + -12.5 = -4.031128874 Simplifying x + -12.5 = -4.031128874 Reorder the terms: -12.5 + x = -4.031128874 Solving -12.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -4.031128874 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -4.031128874 + 12.5 x = -4.031128874 + 12.5 Combine like terms: -4.031128874 + 12.5 = 8.468871126 x = 8.468871126 Simplifying x = 8.468871126Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.531128874, 8.468871126}
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