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Simplifying x(x + 12) = 12 Reorder the terms: x(12 + x) = 12 (12 * x + x * x) = 12 (12x + x2) = 12 Solving 12x + x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 12x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 12x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 12x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 12x + x2 = 0 + 12 12x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 12x + x2 = 12 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 = 12 + 36 Reorder the terms: 36 + 12x + x2 = 12 + 36 Combine like terms: 12 + 36 = 48 36 + 12x + x2 = 48 Factor a perfect square on the left side: (x + 6)(x + 6) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 6) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 6 = 6.92820323 Simplifying x + 6 = 6.92820323 Reorder the terms: 6 + x = 6.92820323 Solving 6 + x = 6.92820323 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 = 6.92820323 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.92820323 + -6 x = 6.92820323 + -6 Combine like terms: 6.92820323 + -6 = 0.92820323 x = 0.92820323 Simplifying x = 0.92820323Subproblem 2
x + 6 = -6.92820323 Simplifying x + 6 = -6.92820323 Reorder the terms: 6 + x = -6.92820323 Solving 6 + x = -6.92820323 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 = -6.92820323 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.92820323 + -6 x = -6.92820323 + -6 Combine like terms: -6.92820323 + -6 = -12.92820323 x = -12.92820323 Simplifying x = -12.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.92820323, -12.92820323}
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