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Simplifying x + x2 = 130 Solving x + x2 = 130 Solving for variable 'x'. Reorder the terms: -130 + x + x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + x + x2 = 0 + 130 x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 x + x2 = 130 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 = 130 + 0.25 Reorder the terms: 0.25 + x + x2 = 130 + 0.25 Combine like terms: 130 + 0.25 = 130.25 0.25 + x + x2 = 130.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + 0.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + 0.5 = 11.412712211 Simplifying x + 0.5 = 11.412712211 Reorder the terms: 0.5 + x = 11.412712211 Solving 0.5 + x = 11.412712211 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 = 11.412712211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.412712211 + -0.5 x = 11.412712211 + -0.5 Combine like terms: 11.412712211 + -0.5 = 10.912712211 x = 10.912712211 Simplifying x = 10.912712211Subproblem 2
x + 0.5 = -11.412712211 Simplifying x + 0.5 = -11.412712211 Reorder the terms: 0.5 + x = -11.412712211 Solving 0.5 + x = -11.412712211 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 = -11.412712211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.412712211 + -0.5 x = -11.412712211 + -0.5 Combine like terms: -11.412712211 + -0.5 = -11.912712211 x = -11.912712211 Simplifying x = -11.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.912712211, -11.912712211}
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