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Simplifying (5k3 + 2k2) + -1(5k2 + -5k3) = 0 Reorder the terms: (2k2 + 5k3) + -1(5k2 + -5k3) = 0 Remove parenthesis around (2k2 + 5k3) 2k2 + 5k3 + -1(5k2 + -5k3) = 0 2k2 + 5k3 + (5k2 * -1 + -5k3 * -1) = 0 2k2 + 5k3 + (-5k2 + 5k3) = 0 Reorder the terms: 2k2 + -5k2 + 5k3 + 5k3 = 0 Combine like terms: 2k2 + -5k2 = -3k2 -3k2 + 5k3 + 5k3 = 0 Combine like terms: 5k3 + 5k3 = 10k3 -3k2 + 10k3 = 0 Solving -3k2 + 10k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k2'. k2(-3 + 10k) = 0Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve: Simplifying k2 = 0 Solving k2 = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k2 = 0 Take the square root of each side: k = {0}Subproblem 2
Set the factor '(-3 + 10k)' equal to zero and attempt to solve: Simplifying -3 + 10k = 0 Solving -3 + 10k = 0 Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 10k = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 10k = 0 + 3 10k = 0 + 3 Combine like terms: 0 + 3 = 3 10k = 3 Divide each side by '10'. k = 0.3 Simplifying k = 0.3Solution
k = {0, 0.3}
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