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Simplifying (8k + 1)(8k + 1) = 0 Reorder the terms: (1 + 8k)(8k + 1) = 0 Reorder the terms: (1 + 8k)(1 + 8k) = 0 Multiply (1 + 8k) * (1 + 8k) (1(1 + 8k) + 8k * (1 + 8k)) = 0 ((1 * 1 + 8k * 1) + 8k * (1 + 8k)) = 0 ((1 + 8k) + 8k * (1 + 8k)) = 0 (1 + 8k + (1 * 8k + 8k * 8k)) = 0 (1 + 8k + (8k + 64k2)) = 0 Combine like terms: 8k + 8k = 16k (1 + 16k + 64k2) = 0 Solving 1 + 16k + 64k2 = 0 Solving for variable 'k'. Factor a trinomial. (1 + 8k)(1 + 8k) = 0Subproblem 1
Set the factor '(1 + 8k)' equal to zero and attempt to solve: Simplifying 1 + 8k = 0 Solving 1 + 8k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 8k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8k = 0 + -1 8k = 0 + -1 Combine like terms: 0 + -1 = -1 8k = -1 Divide each side by '8'. k = -0.125 Simplifying k = -0.125Subproblem 2
Set the factor '(1 + 8k)' equal to zero and attempt to solve: Simplifying 1 + 8k = 0 Solving 1 + 8k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 8k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8k = 0 + -1 8k = 0 + -1 Combine like terms: 0 + -1 = -1 8k = -1 Divide each side by '8'. k = -0.125 Simplifying k = -0.125Solution
k = {-0.125, -0.125}
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