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Simplifying (k + 7)(k + 7) + -1(2k + -5)(2k + -5) = 0 Reorder the terms: (7 + k)(k + 7) + -1(2k + -5)(2k + -5) = 0 Reorder the terms: (7 + k)(7 + k) + -1(2k + -5)(2k + -5) = 0 Multiply (7 + k) * (7 + k) (7(7 + k) + k(7 + k)) + -1(2k + -5)(2k + -5) = 0 ((7 * 7 + k * 7) + k(7 + k)) + -1(2k + -5)(2k + -5) = 0 ((49 + 7k) + k(7 + k)) + -1(2k + -5)(2k + -5) = 0 (49 + 7k + (7 * k + k * k)) + -1(2k + -5)(2k + -5) = 0 (49 + 7k + (7k + k2)) + -1(2k + -5)(2k + -5) = 0 Combine like terms: 7k + 7k = 14k (49 + 14k + k2) + -1(2k + -5)(2k + -5) = 0 Reorder the terms: 49 + 14k + k2 + -1(-5 + 2k)(2k + -5) = 0 Reorder the terms: 49 + 14k + k2 + -1(-5 + 2k)(-5 + 2k) = 0 Multiply (-5 + 2k) * (-5 + 2k) 49 + 14k + k2 + -1(-5(-5 + 2k) + 2k * (-5 + 2k)) = 0 49 + 14k + k2 + -1((-5 * -5 + 2k * -5) + 2k * (-5 + 2k)) = 0 49 + 14k + k2 + -1((25 + -10k) + 2k * (-5 + 2k)) = 0 49 + 14k + k2 + -1(25 + -10k + (-5 * 2k + 2k * 2k)) = 0 49 + 14k + k2 + -1(25 + -10k + (-10k + 4k2)) = 0 Combine like terms: -10k + -10k = -20k 49 + 14k + k2 + -1(25 + -20k + 4k2) = 0 49 + 14k + k2 + (25 * -1 + -20k * -1 + 4k2 * -1) = 0 49 + 14k + k2 + (-25 + 20k + -4k2) = 0 Reorder the terms: 49 + -25 + 14k + 20k + k2 + -4k2 = 0 Combine like terms: 49 + -25 = 24 24 + 14k + 20k + k2 + -4k2 = 0 Combine like terms: 14k + 20k = 34k 24 + 34k + k2 + -4k2 = 0 Combine like terms: k2 + -4k2 = -3k2 24 + 34k + -3k2 = 0 Solving 24 + 34k + -3k2 = 0 Solving for variable 'k'. Factor a trinomial. (12 + -1k)(2 + 3k) = 0Subproblem 1
Set the factor '(12 + -1k)' equal to zero and attempt to solve: Simplifying 12 + -1k = 0 Solving 12 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1k = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1k = 0 + -12 -1k = 0 + -12 Combine like terms: 0 + -12 = -12 -1k = -12 Divide each side by '-1'. k = 12 Simplifying k = 12Subproblem 2
Set the factor '(2 + 3k)' equal to zero and attempt to solve: Simplifying 2 + 3k = 0 Solving 2 + 3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3k = 0 + -2 3k = 0 + -2 Combine like terms: 0 + -2 = -2 3k = -2 Divide each side by '3'. k = -0.6666666667 Simplifying k = -0.6666666667Solution
k = {12, -0.6666666667}
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