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Simplifying 6k4 + 48k3 + 288k2 = 0 Reorder the terms: 288k2 + 48k3 + 6k4 = 0 Solving 288k2 + 48k3 + 6k4 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '6k2'. 6k2(48 + 8k + k2) = 0 Ignore the factor 6.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 '(48 + 8k + k2)' equal to zero and attempt to solve: Simplifying 48 + 8k + k2 = 0 Solving 48 + 8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + 8k + -48 + k2 = 0 + -48 Reorder the terms: 48 + -48 + 8k + k2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 8k + k2 = 0 + -48 8k + k2 = 0 + -48 Combine like terms: 0 + -48 = -48 8k + k2 = -48 The k term is 8k. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8k + 16 + k2 = -48 + 16 Reorder the terms: 16 + 8k + k2 = -48 + 16 Combine like terms: -48 + 16 = -32 16 + 8k + k2 = -32 Factor a perfect square on the left side: (k + 4)(k + 4) = -32 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
k = {0}
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