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Simplifying k(k + -7) + 10 = 2k + k(k + 6) Reorder the terms: k(-7 + k) + 10 = 2k + k(k + 6) (-7 * k + k * k) + 10 = 2k + k(k + 6) (-7k + k2) + 10 = 2k + k(k + 6) Reorder the terms: 10 + -7k + k2 = 2k + k(k + 6) Reorder the terms: 10 + -7k + k2 = 2k + k(6 + k) 10 + -7k + k2 = 2k + (6 * k + k * k) 10 + -7k + k2 = 2k + (6k + k2) Combine like terms: 2k + 6k = 8k 10 + -7k + k2 = 8k + k2 Add '-1k2' to each side of the equation. 10 + -7k + k2 + -1k2 = 8k + k2 + -1k2 Combine like terms: k2 + -1k2 = 0 10 + -7k + 0 = 8k + k2 + -1k2 10 + -7k = 8k + k2 + -1k2 Combine like terms: k2 + -1k2 = 0 10 + -7k = 8k + 0 10 + -7k = 8k Solving 10 + -7k = 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. 10 + -7k + -8k = 8k + -8k Combine like terms: -7k + -8k = -15k 10 + -15k = 8k + -8k Combine like terms: 8k + -8k = 0 10 + -15k = 0 Add '-10' to each side of the equation. 10 + -10 + -15k = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -15k = 0 + -10 -15k = 0 + -10 Combine like terms: 0 + -10 = -10 -15k = -10 Divide each side by '-15'. k = 0.6666666667 Simplifying k = 0.6666666667
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