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Simplifying x(x + 1) = 291 Reorder the terms: x(1 + x) = 291 (1 * x + x * x) = 291 (1x + x2) = 291 Solving 1x + x2 = 291 Solving for variable 'x'. Reorder the terms: -291 + 1x + x2 = 291 + -291 Combine like terms: 291 + -291 = 0 -291 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '291' to each side of the equation. -291 + 1x + 291 + x2 = 0 + 291 Reorder the terms: -291 + 291 + 1x + x2 = 0 + 291 Combine like terms: -291 + 291 = 0 0 + 1x + x2 = 0 + 291 1x + x2 = 0 + 291 Combine like terms: 0 + 291 = 291 1x + x2 = 291 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 = 291 + 0.25 Reorder the terms: 0.25 + x + x2 = 291 + 0.25 Combine like terms: 291 + 0.25 = 291.25 0.25 + x + x2 = 291.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 291.25 Calculate the square root of the right side: 17.066048166 Break this problem into two subproblems by setting (x + 0.5) equal to 17.066048166 and -17.066048166.Subproblem 1
x + 0.5 = 17.066048166 Simplifying x + 0.5 = 17.066048166 Reorder the terms: 0.5 + x = 17.066048166 Solving 0.5 + x = 17.066048166 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 = 17.066048166 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.066048166 + -0.5 x = 17.066048166 + -0.5 Combine like terms: 17.066048166 + -0.5 = 16.566048166 x = 16.566048166 Simplifying x = 16.566048166Subproblem 2
x + 0.5 = -17.066048166 Simplifying x + 0.5 = -17.066048166 Reorder the terms: 0.5 + x = -17.066048166 Solving 0.5 + x = -17.066048166 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 = -17.066048166 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.066048166 + -0.5 x = -17.066048166 + -0.5 Combine like terms: -17.066048166 + -0.5 = -17.566048166 x = -17.566048166 Simplifying x = -17.566048166Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.566048166, -17.566048166}
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