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Simplifying 2k2 + -12k = 37 Reorder the terms: -12k + 2k2 = 37 Solving -12k + 2k2 = 37 Solving for variable 'k'. Reorder the terms: -37 + -12k + 2k2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -12k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18.5 + -6k + k2 = 0 Move the constant term to the right: Add '18.5' to each side of the equation. -18.5 + -6k + 18.5 + k2 = 0 + 18.5 Reorder the terms: -18.5 + 18.5 + -6k + k2 = 0 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + -6k + k2 = 0 + 18.5 -6k + k2 = 0 + 18.5 Combine like terms: 0 + 18.5 = 18.5 -6k + k2 = 18.5 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 = 18.5 + 9 Reorder the terms: 9 + -6k + k2 = 18.5 + 9 Combine like terms: 18.5 + 9 = 27.5 9 + -6k + k2 = 27.5 Factor a perfect square on the left side: (k + -3)(k + -3) = 27.5 Calculate the square root of the right side: 5.244044241 Break this problem into two subproblems by setting (k + -3) equal to 5.244044241 and -5.244044241.Subproblem 1
k + -3 = 5.244044241 Simplifying k + -3 = 5.244044241 Reorder the terms: -3 + k = 5.244044241 Solving -3 + k = 5.244044241 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 = 5.244044241 + 3 Combine like terms: -3 + 3 = 0 0 + k = 5.244044241 + 3 k = 5.244044241 + 3 Combine like terms: 5.244044241 + 3 = 8.244044241 k = 8.244044241 Simplifying k = 8.244044241Subproblem 2
k + -3 = -5.244044241 Simplifying k + -3 = -5.244044241 Reorder the terms: -3 + k = -5.244044241 Solving -3 + k = -5.244044241 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 = -5.244044241 + 3 Combine like terms: -3 + 3 = 0 0 + k = -5.244044241 + 3 k = -5.244044241 + 3 Combine like terms: -5.244044241 + 3 = -2.244044241 k = -2.244044241 Simplifying k = -2.244044241Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.244044241, -2.244044241}
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