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Simplifying x2 + -37x + 140 = 0 Reorder the terms: 140 + -37x + x2 = 0 Solving 140 + -37x + 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 + -37x + -140 + x2 = 0 + -140 Reorder the terms: 140 + -140 + -37x + x2 = 0 + -140 Combine like terms: 140 + -140 = 0 0 + -37x + x2 = 0 + -140 -37x + x2 = 0 + -140 Combine like terms: 0 + -140 = -140 -37x + x2 = -140 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -140 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -140 + 342.25 Combine like terms: -140 + 342.25 = 202.25 342.25 + -37x + x2 = 202.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (x + -18.5) equal to 14.221462653 and -14.221462653.Subproblem 1
x + -18.5 = 14.221462653 Simplifying x + -18.5 = 14.221462653 Reorder the terms: -18.5 + x = 14.221462653 Solving -18.5 + x = 14.221462653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 14.221462653 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 14.221462653 + 18.5 x = 14.221462653 + 18.5 Combine like terms: 14.221462653 + 18.5 = 32.721462653 x = 32.721462653 Simplifying x = 32.721462653Subproblem 2
x + -18.5 = -14.221462653 Simplifying x + -18.5 = -14.221462653 Reorder the terms: -18.5 + x = -14.221462653 Solving -18.5 + x = -14.221462653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -14.221462653 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -14.221462653 + 18.5 x = -14.221462653 + 18.5 Combine like terms: -14.221462653 + 18.5 = 4.278537347 x = 4.278537347 Simplifying x = 4.278537347Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.721462653, 4.278537347}
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