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Simplifying 90k2 + 530k + 400 = 0 Reorder the terms: 400 + 530k + 90k2 = 0 Solving 400 + 530k + 90k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '10'. 10(40 + 53k + 9k2) = 0 Factor a trinomial. 10((5 + k)(8 + 9k)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(5 + k)' equal to zero and attempt to solve: Simplifying 5 + k = 0 Solving 5 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + k = 0 + -5 k = 0 + -5 Combine like terms: 0 + -5 = -5 k = -5 Simplifying k = -5Subproblem 2
Set the factor '(8 + 9k)' equal to zero and attempt to solve: Simplifying 8 + 9k = 0 Solving 8 + 9k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 9k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 9k = 0 + -8 9k = 0 + -8 Combine like terms: 0 + -8 = -8 9k = -8 Divide each side by '9'. k = -0.8888888889 Simplifying k = -0.8888888889Solution
k = {-5, -0.8888888889}
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