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Simplifying x + 18 = 2(x + 4) * 2(x + 1) Reorder the terms: 18 + x = 2(x + 4) * 2(x + 1) Reorder the terms: 18 + x = 2(4 + x) * 2(x + 1) Reorder the terms: 18 + x = 2(4 + x) * 2(1 + x) Reorder the terms for easier multiplication: 18 + x = 2 * 2(4 + x)(1 + x) Multiply 2 * 2 18 + x = 4(4 + x)(1 + x) Multiply (4 + x) * (1 + x) 18 + x = 4(4(1 + x) + x(1 + x)) 18 + x = 4((1 * 4 + x * 4) + x(1 + x)) 18 + x = 4((4 + 4x) + x(1 + x)) 18 + x = 4(4 + 4x + (1 * x + x * x)) 18 + x = 4(4 + 4x + (1x + x2)) Combine like terms: 4x + 1x = 5x 18 + x = 4(4 + 5x + x2) 18 + x = (4 * 4 + 5x * 4 + x2 * 4) 18 + x = (16 + 20x + 4x2) Solving 18 + x = 16 + 20x + 4x2 Solving for variable 'x'. Reorder the terms: 18 + -16 + x + -20x + -4x2 = 16 + 20x + 4x2 + -16 + -20x + -4x2 Combine like terms: 18 + -16 = 2 2 + x + -20x + -4x2 = 16 + 20x + 4x2 + -16 + -20x + -4x2 Combine like terms: x + -20x = -19x 2 + -19x + -4x2 = 16 + 20x + 4x2 + -16 + -20x + -4x2 Reorder the terms: 2 + -19x + -4x2 = 16 + -16 + 20x + -20x + 4x2 + -4x2 Combine like terms: 16 + -16 = 0 2 + -19x + -4x2 = 0 + 20x + -20x + 4x2 + -4x2 2 + -19x + -4x2 = 20x + -20x + 4x2 + -4x2 Combine like terms: 20x + -20x = 0 2 + -19x + -4x2 = 0 + 4x2 + -4x2 2 + -19x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 2 + -19x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.5 + 4.75x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 4.75x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 4.75x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 4.75x + x2 = 0 + 0.5 4.75x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 4.75x + x2 = 0.5 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 0.5 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 0.5 + 5.640625 Combine like terms: 0.5 + 5.640625 = 6.140625 5.640625 + 4.75x + x2 = 6.140625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 6.140625 Calculate the square root of the right side: 2.47802845 Break this problem into two subproblems by setting (x + 2.375) equal to 2.47802845 and -2.47802845.Subproblem 1
x + 2.375 = 2.47802845 Simplifying x + 2.375 = 2.47802845 Reorder the terms: 2.375 + x = 2.47802845 Solving 2.375 + x = 2.47802845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 2.47802845 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 2.47802845 + -2.375 x = 2.47802845 + -2.375 Combine like terms: 2.47802845 + -2.375 = 0.10302845 x = 0.10302845 Simplifying x = 0.10302845Subproblem 2
x + 2.375 = -2.47802845 Simplifying x + 2.375 = -2.47802845 Reorder the terms: 2.375 + x = -2.47802845 Solving 2.375 + x = -2.47802845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -2.47802845 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -2.47802845 + -2.375 x = -2.47802845 + -2.375 Combine like terms: -2.47802845 + -2.375 = -4.85302845 x = -4.85302845 Simplifying x = -4.85302845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.10302845, -4.85302845}
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