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Simplifying x2 + x = 141 Reorder the terms: x + x2 = 141 Solving x + x2 = 141 Solving for variable 'x'. Reorder the terms: -141 + x + x2 = 141 + -141 Combine like terms: 141 + -141 = 0 -141 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '141' to each side of the equation. -141 + x + 141 + x2 = 0 + 141 Reorder the terms: -141 + 141 + x + x2 = 0 + 141 Combine like terms: -141 + 141 = 0 0 + x + x2 = 0 + 141 x + x2 = 0 + 141 Combine like terms: 0 + 141 = 141 x + x2 = 141 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 = 141 + 0.25 Reorder the terms: 0.25 + x + x2 = 141 + 0.25 Combine like terms: 141 + 0.25 = 141.25 0.25 + x + x2 = 141.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 141.25 Calculate the square root of the right side: 11.884864324 Break this problem into two subproblems by setting (x + 0.5) equal to 11.884864324 and -11.884864324.Subproblem 1
x + 0.5 = 11.884864324 Simplifying x + 0.5 = 11.884864324 Reorder the terms: 0.5 + x = 11.884864324 Solving 0.5 + x = 11.884864324 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 = 11.884864324 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.884864324 + -0.5 x = 11.884864324 + -0.5 Combine like terms: 11.884864324 + -0.5 = 11.384864324 x = 11.384864324 Simplifying x = 11.384864324Subproblem 2
x + 0.5 = -11.884864324 Simplifying x + 0.5 = -11.884864324 Reorder the terms: 0.5 + x = -11.884864324 Solving 0.5 + x = -11.884864324 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 = -11.884864324 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.884864324 + -0.5 x = -11.884864324 + -0.5 Combine like terms: -11.884864324 + -0.5 = -12.384864324 x = -12.384864324 Simplifying x = -12.384864324Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.384864324, -12.384864324}
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