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Simplifying x2 + 12x + -244 = 0 Reorder the terms: -244 + 12x + x2 = 0 Solving -244 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '244' to each side of the equation. -244 + 12x + 244 + x2 = 0 + 244 Reorder the terms: -244 + 244 + 12x + x2 = 0 + 244 Combine like terms: -244 + 244 = 0 0 + 12x + x2 = 0 + 244 12x + x2 = 0 + 244 Combine like terms: 0 + 244 = 244 12x + x2 = 244 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 = 244 + 36 Reorder the terms: 36 + 12x + x2 = 244 + 36 Combine like terms: 244 + 36 = 280 36 + 12x + x2 = 280 Factor a perfect square on the left side: (x + 6)(x + 6) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (x + 6) equal to 16.733200531 and -16.733200531.Subproblem 1
x + 6 = 16.733200531 Simplifying x + 6 = 16.733200531 Reorder the terms: 6 + x = 16.733200531 Solving 6 + x = 16.733200531 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 = 16.733200531 + -6 Combine like terms: 6 + -6 = 0 0 + x = 16.733200531 + -6 x = 16.733200531 + -6 Combine like terms: 16.733200531 + -6 = 10.733200531 x = 10.733200531 Simplifying x = 10.733200531Subproblem 2
x + 6 = -16.733200531 Simplifying x + 6 = -16.733200531 Reorder the terms: 6 + x = -16.733200531 Solving 6 + x = -16.733200531 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 = -16.733200531 + -6 Combine like terms: 6 + -6 = 0 0 + x = -16.733200531 + -6 x = -16.733200531 + -6 Combine like terms: -16.733200531 + -6 = -22.733200531 x = -22.733200531 Simplifying x = -22.733200531Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.733200531, -22.733200531}
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