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Simplifying 252 = (x + 1) * x Reorder the terms: 252 = (1 + x) * x Reorder the terms for easier multiplication: 252 = x(1 + x) 252 = (1 * x + x * x) 252 = (1x + x2) Solving 252 = 1x + x2 Solving for variable 'x'. Reorder the terms: 252 + -1x + -1x2 = 1x + -1x + x2 + -1x2 Combine like terms: 1x + -1x = 0 252 + -1x + -1x2 = 0 + x2 + -1x2 252 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 252 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -252 + x + x2 = 0 Move the constant term to the right: Add '252' to each side of the equation. -252 + x + 252 + x2 = 0 + 252 Reorder the terms: -252 + 252 + x + x2 = 0 + 252 Combine like terms: -252 + 252 = 0 0 + x + x2 = 0 + 252 x + x2 = 0 + 252 Combine like terms: 0 + 252 = 252 x + x2 = 252 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. + 0.25 + x2 = 252 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 252 + 0.25 Combine like terms: 252 + 0.25 = 252.25 1.25 + x2 = 252.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 252.25 Calculate the square root of the right side: 15.882380174 Break this problem into two subproblems by setting (x + 0.5) equal to 15.882380174 and -15.882380174.Subproblem 1
x + 0.5 = 15.882380174 Simplifying x + 0.5 = 15.882380174 Reorder the terms: 0.5 + x = 15.882380174 Solving 0.5 + x = 15.882380174 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 = 15.882380174 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 15.882380174 + -0.5 x = 15.882380174 + -0.5 Combine like terms: 15.882380174 + -0.5 = 15.382380174 x = 15.382380174 Simplifying x = 15.382380174Subproblem 2
x + 0.5 = -15.882380174 Simplifying x + 0.5 = -15.882380174 Reorder the terms: 0.5 + x = -15.882380174 Solving 0.5 + x = -15.882380174 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 = -15.882380174 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -15.882380174 + -0.5 x = -15.882380174 + -0.5 Combine like terms: -15.882380174 + -0.5 = -16.382380174 x = -16.382380174 Simplifying x = -16.382380174Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.382380174, -16.382380174}
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