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Simplifying (x + 8)(x + 12) = 288 Reorder the terms: (8 + x)(x + 12) = 288 Reorder the terms: (8 + x)(12 + x) = 288 Multiply (8 + x) * (12 + x) (8(12 + x) + x(12 + x)) = 288 ((12 * 8 + x * 8) + x(12 + x)) = 288 ((96 + 8x) + x(12 + x)) = 288 (96 + 8x + (12 * x + x * x)) = 288 (96 + 8x + (12x + x2)) = 288 Combine like terms: 8x + 12x = 20x (96 + 20x + x2) = 288 Solving 96 + 20x + x2 = 288 Solving for variable 'x'. Reorder the terms: 96 + -288 + 20x + x2 = 288 + -288 Combine like terms: 96 + -288 = -192 -192 + 20x + x2 = 288 + -288 Combine like terms: 288 + -288 = 0 -192 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 20x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 20x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 20x + x2 = 0 + 192 20x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 20x + x2 = 192 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 = 192 + 100 Reorder the terms: 100 + 20x + x2 = 192 + 100 Combine like terms: 192 + 100 = 292 100 + 20x + x2 = 292 Factor a perfect square on the left side: (x + 10)(x + 10) = 292 Calculate the square root of the right side: 17.088007491 Break this problem into two subproblems by setting (x + 10) equal to 17.088007491 and -17.088007491.Subproblem 1
x + 10 = 17.088007491 Simplifying x + 10 = 17.088007491 Reorder the terms: 10 + x = 17.088007491 Solving 10 + x = 17.088007491 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 = 17.088007491 + -10 Combine like terms: 10 + -10 = 0 0 + x = 17.088007491 + -10 x = 17.088007491 + -10 Combine like terms: 17.088007491 + -10 = 7.088007491 x = 7.088007491 Simplifying x = 7.088007491Subproblem 2
x + 10 = -17.088007491 Simplifying x + 10 = -17.088007491 Reorder the terms: 10 + x = -17.088007491 Solving 10 + x = -17.088007491 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 = -17.088007491 + -10 Combine like terms: 10 + -10 = 0 0 + x = -17.088007491 + -10 x = -17.088007491 + -10 Combine like terms: -17.088007491 + -10 = -27.088007491 x = -27.088007491 Simplifying x = -27.088007491Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.088007491, -27.088007491}
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