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Simplifying x(x + 1) = 271 Reorder the terms: x(1 + x) = 271 (1 * x + x * x) = 271 (1x + x2) = 271 Solving 1x + x2 = 271 Solving for variable 'x'. Reorder the terms: -271 + 1x + x2 = 271 + -271 Combine like terms: 271 + -271 = 0 -271 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '271' to each side of the equation. -271 + 1x + 271 + x2 = 0 + 271 Reorder the terms: -271 + 271 + 1x + x2 = 0 + 271 Combine like terms: -271 + 271 = 0 0 + 1x + x2 = 0 + 271 1x + x2 = 0 + 271 Combine like terms: 0 + 271 = 271 1x + x2 = 271 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 = 271 + 0.25 Reorder the terms: 0.25 + x + x2 = 271 + 0.25 Combine like terms: 271 + 0.25 = 271.25 0.25 + x + x2 = 271.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 271.25 Calculate the square root of the right side: 16.469669092 Break this problem into two subproblems by setting (x + 0.5) equal to 16.469669092 and -16.469669092.Subproblem 1
x + 0.5 = 16.469669092 Simplifying x + 0.5 = 16.469669092 Reorder the terms: 0.5 + x = 16.469669092 Solving 0.5 + x = 16.469669092 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 = 16.469669092 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.469669092 + -0.5 x = 16.469669092 + -0.5 Combine like terms: 16.469669092 + -0.5 = 15.969669092 x = 15.969669092 Simplifying x = 15.969669092Subproblem 2
x + 0.5 = -16.469669092 Simplifying x + 0.5 = -16.469669092 Reorder the terms: 0.5 + x = -16.469669092 Solving 0.5 + x = -16.469669092 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 = -16.469669092 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.469669092 + -0.5 x = -16.469669092 + -0.5 Combine like terms: -16.469669092 + -0.5 = -16.969669092 x = -16.969669092 Simplifying x = -16.969669092Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.969669092, -16.969669092}
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