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Simplifying (7k + -3)(7k + 7) = 0 Reorder the terms: (-3 + 7k)(7k + 7) = 0 Reorder the terms: (-3 + 7k)(7 + 7k) = 0 Multiply (-3 + 7k) * (7 + 7k) (-3(7 + 7k) + 7k * (7 + 7k)) = 0 ((7 * -3 + 7k * -3) + 7k * (7 + 7k)) = 0 ((-21 + -21k) + 7k * (7 + 7k)) = 0 (-21 + -21k + (7 * 7k + 7k * 7k)) = 0 (-21 + -21k + (49k + 49k2)) = 0 Combine like terms: -21k + 49k = 28k (-21 + 28k + 49k2) = 0 Solving -21 + 28k + 49k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '7'. 7(-3 + 4k + 7k2) = 0 Factor a trinomial. 7((-1 + -1k)(3 + -7k)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-1 + -1k)' equal to zero and attempt to solve: Simplifying -1 + -1k = 0 Solving -1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1k = 0 + 1 -1k = 0 + 1 Combine like terms: 0 + 1 = 1 -1k = 1 Divide each side by '-1'. k = -1 Simplifying k = -1Subproblem 2
Set the factor '(3 + -7k)' equal to zero and attempt to solve: Simplifying 3 + -7k = 0 Solving 3 + -7k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7k = 0 + -3 -7k = 0 + -3 Combine like terms: 0 + -3 = -3 -7k = -3 Divide each side by '-7'. k = 0.4285714286 Simplifying k = 0.4285714286Solution
k = {-1, 0.4285714286}
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