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Simplifying (x + 12)(x) = 240 Reorder the terms: (12 + x)(x) = 240 Reorder the terms for easier multiplication: x(12 + x) = 240 (12 * x + x * x) = 240 (12x + x2) = 240 Solving 12x + x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 12x + x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 12x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 12x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 12x + x2 = 0 + 240 12x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 12x + x2 = 240 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 240 + 36 Reorder the terms: 36 + 12x + x2 = 240 + 36 Combine like terms: 240 + 36 = 276 36 + 12x + x2 = 276 Factor a perfect square on the left side: (x + 6)(x + 6) = 276 Calculate the square root of the right side: 16.613247726 Break this problem into two subproblems by setting (x + 6) equal to 16.613247726 and -16.613247726.Subproblem 1
x + 6 = 16.613247726 Simplifying x + 6 = 16.613247726 Reorder the terms: 6 + x = 16.613247726 Solving 6 + x = 16.613247726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 16.613247726 + -6 Combine like terms: 6 + -6 = 0 0 + x = 16.613247726 + -6 x = 16.613247726 + -6 Combine like terms: 16.613247726 + -6 = 10.613247726 x = 10.613247726 Simplifying x = 10.613247726Subproblem 2
x + 6 = -16.613247726 Simplifying x + 6 = -16.613247726 Reorder the terms: 6 + x = -16.613247726 Solving 6 + x = -16.613247726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -16.613247726 + -6 Combine like terms: 6 + -6 = 0 0 + x = -16.613247726 + -6 x = -16.613247726 + -6 Combine like terms: -16.613247726 + -6 = -22.613247726 x = -22.613247726 Simplifying x = -22.613247726Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.613247726, -22.613247726}
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