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Simplifying (7 + -1x)(-8 + -1x) + -8k = 0 Multiply (7 + -1x) * (-8 + -1x) (7(-8 + -1x) + -1x * (-8 + -1x)) + -8k = 0 ((-8 * 7 + -1x * 7) + -1x * (-8 + -1x)) + -8k = 0 ((-56 + -7x) + -1x * (-8 + -1x)) + -8k = 0 (-56 + -7x + (-8 * -1x + -1x * -1x)) + -8k = 0 (-56 + -7x + (8x + 1x2)) + -8k = 0 Combine like terms: -7x + 8x = 1x (-56 + 1x + 1x2) + -8k = 0 Reorder the terms: -56 + -8k + 1x + 1x2 = 0 Solving -56 + -8k + 1x + 1x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '56' to each side of the equation. -56 + -8k + 1x + 56 + 1x2 = 0 + 56 Reorder the terms: -56 + 56 + -8k + 1x + 1x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -8k + 1x + 1x2 = 0 + 56 -8k + 1x + 1x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -8k + 1x + 1x2 = 56 Add '-1x' to each side of the equation. -8k + 1x + -1x + 1x2 = 56 + -1x Combine like terms: 1x + -1x = 0 -8k + 0 + 1x2 = 56 + -1x -8k + 1x2 = 56 + -1x Add '-1x2' to each side of the equation. -8k + 1x2 + -1x2 = 56 + -1x + -1x2 Combine like terms: 1x2 + -1x2 = 0 -8k + 0 = 56 + -1x + -1x2 -8k = 56 + -1x + -1x2 Divide each side by '-8'. k = -7 + 0.125x + 0.125x2 Simplifying k = -7 + 0.125x + 0.125x2
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