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Simplifying x + x2 = 25.862 Solving x + x2 = 25.862 Solving for variable 'x'. Reorder the terms: -25.862 + x + x2 = 25.862 + -25.862 Combine like terms: 25.862 + -25.862 = 0.000 -25.862 + x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '25.862' to each side of the equation. -25.862 + x + 25.862 + x2 = 0.000 + 25.862 Reorder the terms: -25.862 + 25.862 + x + x2 = 0.000 + 25.862 Combine like terms: -25.862 + 25.862 = 0.000 0.000 + x + x2 = 0.000 + 25.862 x + x2 = 0.000 + 25.862 Combine like terms: 0.000 + 25.862 = 25.862 x + x2 = 25.862 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 = 25.862 + 0.25 Reorder the terms: 0.25 + x + x2 = 25.862 + 0.25 Combine like terms: 25.862 + 0.25 = 26.112 0.25 + x + x2 = 26.112 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 26.112 Calculate the square root of the right side: 5.109990215 Break this problem into two subproblems by setting (x + 0.5) equal to 5.109990215 and -5.109990215.Subproblem 1
x + 0.5 = 5.109990215 Simplifying x + 0.5 = 5.109990215 Reorder the terms: 0.5 + x = 5.109990215 Solving 0.5 + x = 5.109990215 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 = 5.109990215 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.109990215 + -0.5 x = 5.109990215 + -0.5 Combine like terms: 5.109990215 + -0.5 = 4.609990215 x = 4.609990215 Simplifying x = 4.609990215Subproblem 2
x + 0.5 = -5.109990215 Simplifying x + 0.5 = -5.109990215 Reorder the terms: 0.5 + x = -5.109990215 Solving 0.5 + x = -5.109990215 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 = -5.109990215 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.109990215 + -0.5 x = -5.109990215 + -0.5 Combine like terms: -5.109990215 + -0.5 = -5.609990215 x = -5.609990215 Simplifying x = -5.609990215Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.609990215, -5.609990215}
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