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Simplifying x2 + x + -140 = 0 Reorder the terms: -140 + x + x2 = 0 Solving -140 + x + 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 + x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + x + x2 = 0 + 140 x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 x + x2 = 140 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 140 + 0.25 Reorder the terms: 0.25 + x + x2 = 140 + 0.25 Combine like terms: 140 + 0.25 = 140.25 0.25 + x + x2 = 140.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + 0.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + 0.5 = 11.842719282 Simplifying x + 0.5 = 11.842719282 Reorder the terms: 0.5 + x = 11.842719282 Solving 0.5 + x = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 11.842719282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.842719282 + -0.5 x = 11.842719282 + -0.5 Combine like terms: 11.842719282 + -0.5 = 11.342719282 x = 11.342719282 Simplifying x = 11.342719282Subproblem 2
x + 0.5 = -11.842719282 Simplifying x + 0.5 = -11.842719282 Reorder the terms: 0.5 + x = -11.842719282 Solving 0.5 + x = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -11.842719282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.842719282 + -0.5 x = -11.842719282 + -0.5 Combine like terms: -11.842719282 + -0.5 = -12.342719282 x = -12.342719282 Simplifying x = -12.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.342719282, -12.342719282}
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