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Simplifying 3k2 + -18k + -15 = 0 Reorder the terms: -15 + -18k + 3k2 = 0 Solving -15 + -18k + 3k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -6k + k2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -6k + k2)' equal to zero and attempt to solve: Simplifying -5 + -6k + k2 = 0 Solving -5 + -6k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -6k + 5 + k2 = 0 + 5 Reorder the terms: -5 + 5 + -6k + k2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6k + k2 = 0 + 5 -6k + k2 = 0 + 5 Combine like terms: 0 + 5 = 5 -6k + k2 = 5 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 = 5 + 9 Reorder the terms: 9 + -6k + k2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + -6k + k2 = 14 Factor a perfect square on the left side: (k + -3)(k + -3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (k + -3) equal to 3.741657387 and -3.741657387.Subproblem 1
k + -3 = 3.741657387 Simplifying k + -3 = 3.741657387 Reorder the terms: -3 + k = 3.741657387 Solving -3 + k = 3.741657387 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 = 3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + k = 3.741657387 + 3 k = 3.741657387 + 3 Combine like terms: 3.741657387 + 3 = 6.741657387 k = 6.741657387 Simplifying k = 6.741657387Subproblem 2
k + -3 = -3.741657387 Simplifying k + -3 = -3.741657387 Reorder the terms: -3 + k = -3.741657387 Solving -3 + k = -3.741657387 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 = -3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + k = -3.741657387 + 3 k = -3.741657387 + 3 Combine like terms: -3.741657387 + 3 = -0.741657387 k = -0.741657387 Simplifying k = -0.741657387Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.741657387, -0.741657387}Solution
k = {6.741657387, -0.741657387}
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