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Simplifying (x + 8)(x + 12) = 234 Reorder the terms: (8 + x)(x + 12) = 234 Reorder the terms: (8 + x)(12 + x) = 234 Multiply (8 + x) * (12 + x) (8(12 + x) + x(12 + x)) = 234 ((12 * 8 + x * 8) + x(12 + x)) = 234 ((96 + 8x) + x(12 + x)) = 234 (96 + 8x + (12 * x + x * x)) = 234 (96 + 8x + (12x + x2)) = 234 Combine like terms: 8x + 12x = 20x (96 + 20x + x2) = 234 Solving 96 + 20x + x2 = 234 Solving for variable 'x'. Reorder the terms: 96 + -234 + 20x + x2 = 234 + -234 Combine like terms: 96 + -234 = -138 -138 + 20x + x2 = 234 + -234 Combine like terms: 234 + -234 = 0 -138 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '138' to each side of the equation. -138 + 20x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + 20x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + 20x + x2 = 0 + 138 20x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 20x + x2 = 138 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 138 + 100 Reorder the terms: 100 + 20x + x2 = 138 + 100 Combine like terms: 138 + 100 = 238 100 + 20x + x2 = 238 Factor a perfect square on the left side: (x + 10)(x + 10) = 238 Calculate the square root of the right side: 15.427248621 Break this problem into two subproblems by setting (x + 10) equal to 15.427248621 and -15.427248621.Subproblem 1
x + 10 = 15.427248621 Simplifying x + 10 = 15.427248621 Reorder the terms: 10 + x = 15.427248621 Solving 10 + x = 15.427248621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 15.427248621 + -10 Combine like terms: 10 + -10 = 0 0 + x = 15.427248621 + -10 x = 15.427248621 + -10 Combine like terms: 15.427248621 + -10 = 5.427248621 x = 5.427248621 Simplifying x = 5.427248621Subproblem 2
x + 10 = -15.427248621 Simplifying x + 10 = -15.427248621 Reorder the terms: 10 + x = -15.427248621 Solving 10 + x = -15.427248621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -15.427248621 + -10 Combine like terms: 10 + -10 = 0 0 + x = -15.427248621 + -10 x = -15.427248621 + -10 Combine like terms: -15.427248621 + -10 = -25.427248621 x = -25.427248621 Simplifying x = -25.427248621Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.427248621, -25.427248621}
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