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Simplifying x(x + 2) = 182 Reorder the terms: x(2 + x) = 182 (2 * x + x * x) = 182 (2x + x2) = 182 Solving 2x + x2 = 182 Solving for variable 'x'. Reorder the terms: -182 + 2x + x2 = 182 + -182 Combine like terms: 182 + -182 = 0 -182 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '182' to each side of the equation. -182 + 2x + 182 + x2 = 0 + 182 Reorder the terms: -182 + 182 + 2x + x2 = 0 + 182 Combine like terms: -182 + 182 = 0 0 + 2x + x2 = 0 + 182 2x + x2 = 0 + 182 Combine like terms: 0 + 182 = 182 2x + x2 = 182 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 182 + 1 Reorder the terms: 1 + 2x + x2 = 182 + 1 Combine like terms: 182 + 1 = 183 1 + 2x + x2 = 183 Factor a perfect square on the left side: (x + 1)(x + 1) = 183 Calculate the square root of the right side: 13.527749258 Break this problem into two subproblems by setting (x + 1) equal to 13.527749258 and -13.527749258.Subproblem 1
x + 1 = 13.527749258 Simplifying x + 1 = 13.527749258 Reorder the terms: 1 + x = 13.527749258 Solving 1 + x = 13.527749258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 13.527749258 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.527749258 + -1 x = 13.527749258 + -1 Combine like terms: 13.527749258 + -1 = 12.527749258 x = 12.527749258 Simplifying x = 12.527749258Subproblem 2
x + 1 = -13.527749258 Simplifying x + 1 = -13.527749258 Reorder the terms: 1 + x = -13.527749258 Solving 1 + x = -13.527749258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -13.527749258 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.527749258 + -1 x = -13.527749258 + -1 Combine like terms: -13.527749258 + -1 = -14.527749258 x = -14.527749258 Simplifying x = -14.527749258Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.527749258, -14.527749258}
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