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Simplifying (x + 2)(x + 7) + k = 0 Reorder the terms: (2 + x)(x + 7) + k = 0 Reorder the terms: (2 + x)(7 + x) + k = 0 Multiply (2 + x) * (7 + x) (2(7 + x) + x(7 + x)) + k = 0 ((7 * 2 + x * 2) + x(7 + x)) + k = 0 ((14 + 2x) + x(7 + x)) + k = 0 (14 + 2x + (7 * x + x * x)) + k = 0 (14 + 2x + (7x + x2)) + k = 0 Combine like terms: 2x + 7x = 9x (14 + 9x + x2) + k = 0 Reorder the terms: 14 + k + 9x + x2 = 0 Solving 14 + k + 9x + x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + k + 9x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + k + 9x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + k + 9x + x2 = 0 + -14 k + 9x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 k + 9x + x2 = -14 Add '-9x' to each side of the equation. k + 9x + -9x + x2 = -14 + -9x Combine like terms: 9x + -9x = 0 k + 0 + x2 = -14 + -9x k + x2 = -14 + -9x Add '-1x2' to each side of the equation. k + x2 + -1x2 = -14 + -9x + -1x2 Combine like terms: x2 + -1x2 = 0 k + 0 = -14 + -9x + -1x2 k = -14 + -9x + -1x2 Simplifying k = -14 + -9x + -1x2
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