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Simplifying (12 + 2x)(8 + 2x) = 129 Multiply (12 + 2x) * (8 + 2x) (12(8 + 2x) + 2x * (8 + 2x)) = 129 ((8 * 12 + 2x * 12) + 2x * (8 + 2x)) = 129 ((96 + 24x) + 2x * (8 + 2x)) = 129 (96 + 24x + (8 * 2x + 2x * 2x)) = 129 (96 + 24x + (16x + 4x2)) = 129 Combine like terms: 24x + 16x = 40x (96 + 40x + 4x2) = 129 Solving 96 + 40x + 4x2 = 129 Solving for variable 'x'. Reorder the terms: 96 + -129 + 40x + 4x2 = 129 + -129 Combine like terms: 96 + -129 = -33 -33 + 40x + 4x2 = 129 + -129 Combine like terms: 129 + -129 = 0 -33 + 40x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.25 + 10x + x2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + 10x + 8.25 + x2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + 10x + x2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + 10x + x2 = 0 + 8.25 10x + x2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 10x + x2 = 8.25 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 8.25 + 25 Reorder the terms: 25 + 10x + x2 = 8.25 + 25 Combine like terms: 8.25 + 25 = 33.25 25 + 10x + x2 = 33.25 Factor a perfect square on the left side: (x + 5)(x + 5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + 5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + 5 = 5.766281297 Simplifying x + 5 = 5.766281297 Reorder the terms: 5 + x = 5.766281297 Solving 5 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.766281297 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.766281297 + -5 x = 5.766281297 + -5 Combine like terms: 5.766281297 + -5 = 0.766281297 x = 0.766281297 Simplifying x = 0.766281297Subproblem 2
x + 5 = -5.766281297 Simplifying x + 5 = -5.766281297 Reorder the terms: 5 + x = -5.766281297 Solving 5 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.766281297 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.766281297 + -5 x = -5.766281297 + -5 Combine like terms: -5.766281297 + -5 = -10.766281297 x = -10.766281297 Simplifying x = -10.766281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.766281297, -10.766281297}
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