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Simplifying k2 + -12k = -12 Reorder the terms: -12k + k2 = -12 Solving -12k + k2 = -12 Solving for variable 'k'. Reorder the terms: 12 + -12k + k2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -12k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -12k + -12 + k2 = 0 + -12 Reorder the terms: 12 + -12 + -12k + k2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -12k + k2 = 0 + -12 -12k + k2 = 0 + -12 Combine like terms: 0 + -12 = -12 -12k + k2 = -12 The k term is -12k. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12k + 36 + k2 = -12 + 36 Reorder the terms: 36 + -12k + k2 = -12 + 36 Combine like terms: -12 + 36 = 24 36 + -12k + k2 = 24 Factor a perfect square on the left side: (k + -6)(k + -6) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (k + -6) equal to 4.898979486 and -4.898979486.Subproblem 1
k + -6 = 4.898979486 Simplifying k + -6 = 4.898979486 Reorder the terms: -6 + k = 4.898979486 Solving -6 + k = 4.898979486 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + k = 4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + k = 4.898979486 + 6 k = 4.898979486 + 6 Combine like terms: 4.898979486 + 6 = 10.898979486 k = 10.898979486 Simplifying k = 10.898979486Subproblem 2
k + -6 = -4.898979486 Simplifying k + -6 = -4.898979486 Reorder the terms: -6 + k = -4.898979486 Solving -6 + k = -4.898979486 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + k = -4.898979486 + 6 Combine like terms: -6 + 6 = 0 0 + k = -4.898979486 + 6 k = -4.898979486 + 6 Combine like terms: -4.898979486 + 6 = 1.101020514 k = 1.101020514 Simplifying k = 1.101020514Solution
The solution to the problem is based on the solutions from the subproblems. k = {10.898979486, 1.101020514}
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