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Simplifying x(x + 12) = 30 Reorder the terms: x(12 + x) = 30 (12 * x + x * x) = 30 (12x + x2) = 30 Solving 12x + x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 12x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 12x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 12x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 12x + x2 = 0 + 30 12x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 12x + x2 = 30 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 = 30 + 36 Reorder the terms: 36 + 12x + x2 = 30 + 36 Combine like terms: 30 + 36 = 66 36 + 12x + x2 = 66 Factor a perfect square on the left side: (x + 6)(x + 6) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + 6) equal to 8.124038405 and -8.124038405.Subproblem 1
x + 6 = 8.124038405 Simplifying x + 6 = 8.124038405 Reorder the terms: 6 + x = 8.124038405 Solving 6 + x = 8.124038405 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 = 8.124038405 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.124038405 + -6 x = 8.124038405 + -6 Combine like terms: 8.124038405 + -6 = 2.124038405 x = 2.124038405 Simplifying x = 2.124038405Subproblem 2
x + 6 = -8.124038405 Simplifying x + 6 = -8.124038405 Reorder the terms: 6 + x = -8.124038405 Solving 6 + x = -8.124038405 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 = -8.124038405 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.124038405 + -6 x = -8.124038405 + -6 Combine like terms: -8.124038405 + -6 = -14.124038405 x = -14.124038405 Simplifying x = -14.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.124038405, -14.124038405}
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