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Simplifying x2 + -25x + -1140 = 0 Reorder the terms: -1140 + -25x + x2 = 0 Solving -1140 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1140' to each side of the equation. -1140 + -25x + 1140 + x2 = 0 + 1140 Reorder the terms: -1140 + 1140 + -25x + x2 = 0 + 1140 Combine like terms: -1140 + 1140 = 0 0 + -25x + x2 = 0 + 1140 -25x + x2 = 0 + 1140 Combine like terms: 0 + 1140 = 1140 -25x + x2 = 1140 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 = 1140 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 1140 + 156.25 Combine like terms: 1140 + 156.25 = 1296.25 156.25 + -25x + x2 = 1296.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 1296.25 Calculate the square root of the right side: 36.003472055 Break this problem into two subproblems by setting (x + -12.5) equal to 36.003472055 and -36.003472055.Subproblem 1
x + -12.5 = 36.003472055 Simplifying x + -12.5 = 36.003472055 Reorder the terms: -12.5 + x = 36.003472055 Solving -12.5 + x = 36.003472055 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 = 36.003472055 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 36.003472055 + 12.5 x = 36.003472055 + 12.5 Combine like terms: 36.003472055 + 12.5 = 48.503472055 x = 48.503472055 Simplifying x = 48.503472055Subproblem 2
x + -12.5 = -36.003472055 Simplifying x + -12.5 = -36.003472055 Reorder the terms: -12.5 + x = -36.003472055 Solving -12.5 + x = -36.003472055 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 = -36.003472055 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -36.003472055 + 12.5 x = -36.003472055 + 12.5 Combine like terms: -36.003472055 + 12.5 = -23.503472055 x = -23.503472055 Simplifying x = -23.503472055Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.503472055, -23.503472055}
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