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Simplifying x2 + 12x + -289 = 0 Reorder the terms: -289 + 12x + x2 = 0 Solving -289 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '289' to each side of the equation. -289 + 12x + 289 + x2 = 0 + 289 Reorder the terms: -289 + 289 + 12x + x2 = 0 + 289 Combine like terms: -289 + 289 = 0 0 + 12x + x2 = 0 + 289 12x + x2 = 0 + 289 Combine like terms: 0 + 289 = 289 12x + x2 = 289 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 = 289 + 36 Reorder the terms: 36 + 12x + x2 = 289 + 36 Combine like terms: 289 + 36 = 325 36 + 12x + x2 = 325 Factor a perfect square on the left side: (x + 6)(x + 6) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + 6) equal to 18.027756377 and -18.027756377.Subproblem 1
x + 6 = 18.027756377 Simplifying x + 6 = 18.027756377 Reorder the terms: 6 + x = 18.027756377 Solving 6 + x = 18.027756377 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 = 18.027756377 + -6 Combine like terms: 6 + -6 = 0 0 + x = 18.027756377 + -6 x = 18.027756377 + -6 Combine like terms: 18.027756377 + -6 = 12.027756377 x = 12.027756377 Simplifying x = 12.027756377Subproblem 2
x + 6 = -18.027756377 Simplifying x + 6 = -18.027756377 Reorder the terms: 6 + x = -18.027756377 Solving 6 + x = -18.027756377 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 = -18.027756377 + -6 Combine like terms: 6 + -6 = 0 0 + x = -18.027756377 + -6 x = -18.027756377 + -6 Combine like terms: -18.027756377 + -6 = -24.027756377 x = -24.027756377 Simplifying x = -24.027756377Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.027756377, -24.027756377}
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