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Simplifying 12k4 + 22k3 + -70k2 = 0 Reorder the terms: -70k2 + 22k3 + 12k4 = 0 Solving -70k2 + 22k3 + 12k4 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2k2'. 2k2(-35 + 11k + 6k2) = 0 Factor a trinomial. 2k2((-7 + -2k)(5 + -3k)) = 0 Ignore the factor 2.Subproblem 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 '(-7 + -2k)' equal to zero and attempt to solve: Simplifying -7 + -2k = 0 Solving -7 + -2k = 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 + -2k = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2k = 0 + 7 -2k = 0 + 7 Combine like terms: 0 + 7 = 7 -2k = 7 Divide each side by '-2'. k = -3.5 Simplifying k = -3.5Subproblem 3
Set the factor '(5 + -3k)' equal to zero and attempt to solve: Simplifying 5 + -3k = 0 Solving 5 + -3k = 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 + -3k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3k = 0 + -5 -3k = 0 + -5 Combine like terms: 0 + -5 = -5 -3k = -5 Divide each side by '-3'. k = 1.666666667 Simplifying k = 1.666666667Solution
k = {0, -3.5, 1.666666667}
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