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Simplifying 0 = 4k2 + 28k + 49 Reorder the terms: 0 = 49 + 28k + 4k2 Solving 0 = 49 + 28k + 4k2 Solving for variable 'k'. Combine like terms: 0 + -49 = -49 -49 + -28k + -4k2 = 49 + 28k + 4k2 + -49 + -28k + -4k2 Reorder the terms: -49 + -28k + -4k2 = 49 + -49 + 28k + -28k + 4k2 + -4k2 Combine like terms: 49 + -49 = 0 -49 + -28k + -4k2 = 0 + 28k + -28k + 4k2 + -4k2 -49 + -28k + -4k2 = 28k + -28k + 4k2 + -4k2 Combine like terms: 28k + -28k = 0 -49 + -28k + -4k2 = 0 + 4k2 + -4k2 -49 + -28k + -4k2 = 4k2 + -4k2 Combine like terms: 4k2 + -4k2 = 0 -49 + -28k + -4k2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(49 + 28k + 4k2) = 0 Factor a trinomial. -1((7 + 2k)(7 + 2k)) = 0 Ignore the factor -1.Subproblem 1
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 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 = -3.5Solution
k = {-3.5, -3.5}
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