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Simplifying k4 + -100k2 = 0 Reorder the terms: -100k2 + k4 = 0 Solving -100k2 + k4 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k2'. k2(-100 + k2) = 0 Factor a difference between two squares. k2((10 + k)(-10 + k)) = 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 '(10 + k)' equal to zero and attempt to solve: Simplifying 10 + k = 0 Solving 10 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + k = 0 + -10 Combine like terms: 10 + -10 = 0 0 + k = 0 + -10 k = 0 + -10 Combine like terms: 0 + -10 = -10 k = -10 Simplifying k = -10Subproblem 3
Set the factor '(-10 + k)' equal to zero and attempt to solve: Simplifying -10 + k = 0 Solving -10 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + k = 0 + 10 Combine like terms: -10 + 10 = 0 0 + k = 0 + 10 k = 0 + 10 Combine like terms: 0 + 10 = 10 k = 10 Simplifying k = 10Solution
k = {0, -10, 10}
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