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Simplifying x(x + 1) = 60 Reorder the terms: x(1 + x) = 60 (1 * x + x * x) = 60 (1x + x2) = 60 Solving 1x + x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + 1x + x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 1x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 1x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 1x + x2 = 0 + 60 1x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 1x + x2 = 60 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 = 60 + 0.25 Reorder the terms: 0.25 + x + x2 = 60 + 0.25 Combine like terms: 60 + 0.25 = 60.25 0.25 + x + x2 = 60.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + 0.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + 0.5 = 7.762087348 Simplifying x + 0.5 = 7.762087348 Reorder the terms: 0.5 + x = 7.762087348 Solving 0.5 + x = 7.762087348 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 = 7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.762087348 + -0.5 x = 7.762087348 + -0.5 Combine like terms: 7.762087348 + -0.5 = 7.262087348 x = 7.262087348 Simplifying x = 7.262087348Subproblem 2
x + 0.5 = -7.762087348 Simplifying x + 0.5 = -7.762087348 Reorder the terms: 0.5 + x = -7.762087348 Solving 0.5 + x = -7.762087348 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 = -7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.762087348 + -0.5 x = -7.762087348 + -0.5 Combine like terms: -7.762087348 + -0.5 = -8.262087348 x = -8.262087348 Simplifying x = -8.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.262087348, -8.262087348}
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