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Simplifying 3k2 + 18k = 3 Reorder the terms: 18k + 3k2 = 3 Solving 18k + 3k2 = 3 Solving for variable 'k'. Reorder the terms: -3 + 18k + 3k2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 18k + 3k2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 6k + k2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 6k + k2)' equal to zero and attempt to solve: Simplifying -1 + 6k + k2 = 0 Solving -1 + 6k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 6k + 1 + k2 = 0 + 1 Reorder the terms: -1 + 1 + 6k + k2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6k + k2 = 0 + 1 6k + k2 = 0 + 1 Combine like terms: 0 + 1 = 1 6k + k2 = 1 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 = 1 + 9 Reorder the terms: 9 + 6k + k2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + 6k + k2 = 10 Factor a perfect square on the left side: (k + 3)(k + 3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (k + 3) equal to 3.16227766 and -3.16227766.Subproblem 1
k + 3 = 3.16227766 Simplifying k + 3 = 3.16227766 Reorder the terms: 3 + k = 3.16227766 Solving 3 + k = 3.16227766 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 = 3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + k = 3.16227766 + -3 k = 3.16227766 + -3 Combine like terms: 3.16227766 + -3 = 0.16227766 k = 0.16227766 Simplifying k = 0.16227766Subproblem 2
k + 3 = -3.16227766 Simplifying k + 3 = -3.16227766 Reorder the terms: 3 + k = -3.16227766 Solving 3 + k = -3.16227766 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 = -3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + k = -3.16227766 + -3 k = -3.16227766 + -3 Combine like terms: -3.16227766 + -3 = -6.16227766 k = -6.16227766 Simplifying k = -6.16227766Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.16227766, -6.16227766}Solution
k = {0.16227766, -6.16227766}
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