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Simplifying 16x2 + -4k2x2 + 12kx2 = 0 Reorder the terms: 12kx2 + -4k2x2 + 16x2 = 0 Solving 12kx2 + -4k2x2 + 16x2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(3k + -1k2 + 4) = 0 Factor a trinomial. 4x2((-1k + -1)(k + -4)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 = 0 + -1x2 Remove the zero: 0 = -1x2 Simplifying 0 = -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1k + -1)' equal to zero and attempt to solve: Simplifying -1k + -1 = 0 Reorder the terms: -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 3
Set the factor '(k + -4)' equal to zero and attempt to solve: Simplifying k + -4 = 0 Reorder the terms: -4 + k = 0 Solving -4 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + k = 0 + 4 k = 0 + 4 Combine like terms: 0 + 4 = 4 k = 4 Simplifying k = 4Solution
k = {-1, 4}
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