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Simplifying x2 + x = 102 Reorder the terms: x + x2 = 102 Solving x + x2 = 102 Solving for variable 'x'. Reorder the terms: -102 + x + x2 = 102 + -102 Combine like terms: 102 + -102 = 0 -102 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + x + x2 = 0 + 102 x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 x + x2 = 102 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 = 102 + 0.25 Reorder the terms: 0.25 + x + x2 = 102 + 0.25 Combine like terms: 102 + 0.25 = 102.25 0.25 + x + x2 = 102.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (x + 0.5) equal to 10.111874208 and -10.111874208.Subproblem 1
x + 0.5 = 10.111874208 Simplifying x + 0.5 = 10.111874208 Reorder the terms: 0.5 + x = 10.111874208 Solving 0.5 + x = 10.111874208 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 = 10.111874208 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.111874208 + -0.5 x = 10.111874208 + -0.5 Combine like terms: 10.111874208 + -0.5 = 9.611874208 x = 9.611874208 Simplifying x = 9.611874208Subproblem 2
x + 0.5 = -10.111874208 Simplifying x + 0.5 = -10.111874208 Reorder the terms: 0.5 + x = -10.111874208 Solving 0.5 + x = -10.111874208 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 = -10.111874208 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.111874208 + -0.5 x = -10.111874208 + -0.5 Combine like terms: -10.111874208 + -0.5 = -10.611874208 x = -10.611874208 Simplifying x = -10.611874208Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.611874208, -10.611874208}
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