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Simplifying 3k2 + -18k + 12 = 0 Reorder the terms: 12 + -18k + 3k2 = 0 Solving 12 + -18k + 3k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -6k + k2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -6k + k2)' equal to zero and attempt to solve: Simplifying 4 + -6k + k2 = 0 Solving 4 + -6k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6k + -4 + k2 = 0 + -4 Reorder the terms: 4 + -4 + -6k + k2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6k + k2 = 0 + -4 -6k + k2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6k + k2 = -4 The k term is -6k. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6k + 9 + k2 = -4 + 9 Reorder the terms: 9 + -6k + k2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6k + k2 = 5 Factor a perfect square on the left side: (k + -3)(k + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (k + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
k + -3 = 2.236067978 Simplifying k + -3 = 2.236067978 Reorder the terms: -3 + k = 2.236067978 Solving -3 + k = 2.236067978 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + k = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + k = 2.236067978 + 3 k = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 k = 5.236067978 Simplifying k = 5.236067978Subproblem 2
k + -3 = -2.236067978 Simplifying k + -3 = -2.236067978 Reorder the terms: -3 + k = -2.236067978 Solving -3 + k = -2.236067978 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + k = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + k = -2.236067978 + 3 k = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 k = 0.763932022 Simplifying k = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.236067978, 0.763932022}Solution
k = {5.236067978, 0.763932022}
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