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Simplifying x(x + 18) = (x + 9) * 2 Reorder the terms: x(18 + x) = (x + 9) * 2 (18 * x + x * x) = (x + 9) * 2 (18x + x2) = (x + 9) * 2 Reorder the terms: 18x + x2 = (9 + x) * 2 Reorder the terms for easier multiplication: 18x + x2 = 2(9 + x) 18x + x2 = (9 * 2 + x * 2) 18x + x2 = (18 + 2x) Solving 18x + x2 = 18 + 2x Solving for variable 'x'. Reorder the terms: -18 + 18x + -2x + x2 = 18 + 2x + -18 + -2x Combine like terms: 18x + -2x = 16x -18 + 16x + x2 = 18 + 2x + -18 + -2x Reorder the terms: -18 + 16x + x2 = 18 + -18 + 2x + -2x Combine like terms: 18 + -18 = 0 -18 + 16x + x2 = 0 + 2x + -2x -18 + 16x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -18 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 16x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 16x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 16x + x2 = 0 + 18 16x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 16x + x2 = 18 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 = 18 + 64 Reorder the terms: 64 + 16x + x2 = 18 + 64 Combine like terms: 18 + 64 = 82 64 + 16x + x2 = 82 Factor a perfect square on the left side: (x + 8)(x + 8) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x + 8) equal to 9.055385138 and -9.055385138.Subproblem 1
x + 8 = 9.055385138 Simplifying x + 8 = 9.055385138 Reorder the terms: 8 + x = 9.055385138 Solving 8 + x = 9.055385138 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 = 9.055385138 + -8 Combine like terms: 8 + -8 = 0 0 + x = 9.055385138 + -8 x = 9.055385138 + -8 Combine like terms: 9.055385138 + -8 = 1.055385138 x = 1.055385138 Simplifying x = 1.055385138Subproblem 2
x + 8 = -9.055385138 Simplifying x + 8 = -9.055385138 Reorder the terms: 8 + x = -9.055385138 Solving 8 + x = -9.055385138 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 = -9.055385138 + -8 Combine like terms: 8 + -8 = 0 0 + x = -9.055385138 + -8 x = -9.055385138 + -8 Combine like terms: -9.055385138 + -8 = -17.055385138 x = -17.055385138 Simplifying x = -17.055385138Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.055385138, -17.055385138}
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