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Simplifying (x + -2)(x + -7) + -1k = 0 Reorder the terms: (-2 + x)(x + -7) + -1k = 0 Reorder the terms: (-2 + x)(-7 + x) + -1k = 0 Multiply (-2 + x) * (-7 + x) (-2(-7 + x) + x(-7 + x)) + -1k = 0 ((-7 * -2 + x * -2) + x(-7 + x)) + -1k = 0 ((14 + -2x) + x(-7 + x)) + -1k = 0 (14 + -2x + (-7 * x + x * x)) + -1k = 0 (14 + -2x + (-7x + x2)) + -1k = 0 Combine like terms: -2x + -7x = -9x (14 + -9x + x2) + -1k = 0 Reorder the terms: 14 + -1k + -9x + x2 = 0 Solving 14 + -1k + -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 + -1k + -9x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -1k + -9x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1k + -9x + x2 = 0 + -14 -1k + -9x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -1k + -9x + x2 = -14 Add '9x' to each side of the equation. -1k + -9x + 9x + x2 = -14 + 9x Combine like terms: -9x + 9x = 0 -1k + 0 + x2 = -14 + 9x -1k + x2 = -14 + 9x Add '-1x2' to each side of the equation. -1k + x2 + -1x2 = -14 + 9x + -1x2 Combine like terms: x2 + -1x2 = 0 -1k + 0 = -14 + 9x + -1x2 -1k = -14 + 9x + -1x2 Divide each side by '-1'. k = 14 + -9x + x2 Simplifying k = 14 + -9x + x2
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