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Simplifying (x + 12)(x) = 576 Reorder the terms: (12 + x)(x) = 576 Reorder the terms for easier multiplication: x(12 + x) = 576 (12 * x + x * x) = 576 (12x + x2) = 576 Solving 12x + x2 = 576 Solving for variable 'x'. Reorder the terms: -576 + 12x + x2 = 576 + -576 Combine like terms: 576 + -576 = 0 -576 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + 12x + 576 + x2 = 0 + 576 Reorder the terms: -576 + 576 + 12x + x2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + 12x + x2 = 0 + 576 12x + x2 = 0 + 576 Combine like terms: 0 + 576 = 576 12x + x2 = 576 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 = 576 + 36 Reorder the terms: 36 + 12x + x2 = 576 + 36 Combine like terms: 576 + 36 = 612 36 + 12x + x2 = 612 Factor a perfect square on the left side: (x + 6)(x + 6) = 612 Calculate the square root of the right side: 24.738633754 Break this problem into two subproblems by setting (x + 6) equal to 24.738633754 and -24.738633754.Subproblem 1
x + 6 = 24.738633754 Simplifying x + 6 = 24.738633754 Reorder the terms: 6 + x = 24.738633754 Solving 6 + x = 24.738633754 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 = 24.738633754 + -6 Combine like terms: 6 + -6 = 0 0 + x = 24.738633754 + -6 x = 24.738633754 + -6 Combine like terms: 24.738633754 + -6 = 18.738633754 x = 18.738633754 Simplifying x = 18.738633754Subproblem 2
x + 6 = -24.738633754 Simplifying x + 6 = -24.738633754 Reorder the terms: 6 + x = -24.738633754 Solving 6 + x = -24.738633754 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 = -24.738633754 + -6 Combine like terms: 6 + -6 = 0 0 + x = -24.738633754 + -6 x = -24.738633754 + -6 Combine like terms: -24.738633754 + -6 = -30.738633754 x = -30.738633754 Simplifying x = -30.738633754Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.738633754, -30.738633754}
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