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Simplifying x(x + 2) = 180 Reorder the terms: x(2 + x) = 180 (2 * x + x * x) = 180 (2x + x2) = 180 Solving 2x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 2x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 2x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 2x + x2 = 0 + 180 2x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 2x + x2 = 180 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 = 180 + 1 Reorder the terms: 1 + 2x + x2 = 180 + 1 Combine like terms: 180 + 1 = 181 1 + 2x + x2 = 181 Factor a perfect square on the left side: (x + 1)(x + 1) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (x + 1) equal to 13.453624047 and -13.453624047.Subproblem 1
x + 1 = 13.453624047 Simplifying x + 1 = 13.453624047 Reorder the terms: 1 + x = 13.453624047 Solving 1 + x = 13.453624047 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 = 13.453624047 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.453624047 + -1 x = 13.453624047 + -1 Combine like terms: 13.453624047 + -1 = 12.453624047 x = 12.453624047 Simplifying x = 12.453624047Subproblem 2
x + 1 = -13.453624047 Simplifying x + 1 = -13.453624047 Reorder the terms: 1 + x = -13.453624047 Solving 1 + x = -13.453624047 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 = -13.453624047 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.453624047 + -1 x = -13.453624047 + -1 Combine like terms: -13.453624047 + -1 = -14.453624047 x = -14.453624047 Simplifying x = -14.453624047Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.453624047, -14.453624047}
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