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Simplifying x(x + 1) = 118 Reorder the terms: x(1 + x) = 118 (1 * x + x * x) = 118 (1x + x2) = 118 Solving 1x + x2 = 118 Solving for variable 'x'. Reorder the terms: -118 + 1x + x2 = 118 + -118 Combine like terms: 118 + -118 = 0 -118 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + 1x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 1x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 1x + x2 = 0 + 118 1x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 1x + x2 = 118 The x term is 1x. 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 = 118 + 0.25 Reorder the terms: 0.25 + x + x2 = 118 + 0.25 Combine like terms: 118 + 0.25 = 118.25 0.25 + x + x2 = 118.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 118.25 Calculate the square root of the right side: 10.874281585 Break this problem into two subproblems by setting (x + 0.5) equal to 10.874281585 and -10.874281585.Subproblem 1
x + 0.5 = 10.874281585 Simplifying x + 0.5 = 10.874281585 Reorder the terms: 0.5 + x = 10.874281585 Solving 0.5 + x = 10.874281585 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 = 10.874281585 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.874281585 + -0.5 x = 10.874281585 + -0.5 Combine like terms: 10.874281585 + -0.5 = 10.374281585 x = 10.374281585 Simplifying x = 10.374281585Subproblem 2
x + 0.5 = -10.874281585 Simplifying x + 0.5 = -10.874281585 Reorder the terms: 0.5 + x = -10.874281585 Solving 0.5 + x = -10.874281585 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 = -10.874281585 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.874281585 + -0.5 x = -10.874281585 + -0.5 Combine like terms: -10.874281585 + -0.5 = -11.374281585 x = -11.374281585 Simplifying x = -11.374281585Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.374281585, -11.374281585}
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