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Simplifying 5k2 + 75k + 280 = 0 Reorder the terms: 280 + 75k + 5k2 = 0 Solving 280 + 75k + 5k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '5'. 5(56 + 15k + k2) = 0 Factor a trinomial. 5((8 + k)(7 + k)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8 + k)' equal to zero and attempt to solve: Simplifying 8 + k = 0 Solving 8 + k = 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 + k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + k = 0 + -8 k = 0 + -8 Combine like terms: 0 + -8 = -8 k = -8 Simplifying k = -8Subproblem 2
Set the factor '(7 + k)' equal to zero and attempt to solve: Simplifying 7 + k = 0 Solving 7 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + k = 0 + -7 k = 0 + -7 Combine like terms: 0 + -7 = -7 k = -7 Simplifying k = -7Solution
k = {-8, -7}
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