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Simplifying x(x + 15) + (x + 18) = 180 Reorder the terms: x(15 + x) + (x + 18) = 180 (15 * x + x * x) + (x + 18) = 180 (15x + x2) + (x + 18) = 180 Reorder the terms: 15x + x2 + (18 + x) = 180 Remove parenthesis around (18 + x) 15x + x2 + 18 + x = 180 Reorder the terms: 18 + 15x + x + x2 = 180 Combine like terms: 15x + x = 16x 18 + 16x + x2 = 180 Solving 18 + 16x + x2 = 180 Solving for variable 'x'. Reorder the terms: 18 + -180 + 16x + x2 = 180 + -180 Combine like terms: 18 + -180 = -162 -162 + 16x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -162 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + 16x + 162 + x2 = 0 + 162 Reorder the terms: -162 + 162 + 16x + x2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + 16x + x2 = 0 + 162 16x + x2 = 0 + 162 Combine like terms: 0 + 162 = 162 16x + x2 = 162 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 162 + 64 Reorder the terms: 64 + 16x + x2 = 162 + 64 Combine like terms: 162 + 64 = 226 64 + 16x + x2 = 226 Factor a perfect square on the left side: (x + 8)(x + 8) = 226 Calculate the square root of the right side: 15.033296378 Break this problem into two subproblems by setting (x + 8) equal to 15.033296378 and -15.033296378.Subproblem 1
x + 8 = 15.033296378 Simplifying x + 8 = 15.033296378 Reorder the terms: 8 + x = 15.033296378 Solving 8 + x = 15.033296378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 15.033296378 + -8 Combine like terms: 8 + -8 = 0 0 + x = 15.033296378 + -8 x = 15.033296378 + -8 Combine like terms: 15.033296378 + -8 = 7.033296378 x = 7.033296378 Simplifying x = 7.033296378Subproblem 2
x + 8 = -15.033296378 Simplifying x + 8 = -15.033296378 Reorder the terms: 8 + x = -15.033296378 Solving 8 + x = -15.033296378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -15.033296378 + -8 Combine like terms: 8 + -8 = 0 0 + x = -15.033296378 + -8 x = -15.033296378 + -8 Combine like terms: -15.033296378 + -8 = -23.033296378 x = -23.033296378 Simplifying x = -23.033296378Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.033296378, -23.033296378}
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