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Simplifying k2 + 12k + -14 = 0 Reorder the terms: -14 + 12k + k2 = 0 Solving -14 + 12k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 12k + 14 + k2 = 0 + 14 Reorder the terms: -14 + 14 + 12k + k2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 12k + k2 = 0 + 14 12k + k2 = 0 + 14 Combine like terms: 0 + 14 = 14 12k + k2 = 14 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 = 14 + 36 Reorder the terms: 36 + 12k + k2 = 14 + 36 Combine like terms: 14 + 36 = 50 36 + 12k + k2 = 50 Factor a perfect square on the left side: (k + 6)(k + 6) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (k + 6) equal to 7.071067812 and -7.071067812.Subproblem 1
k + 6 = 7.071067812 Simplifying k + 6 = 7.071067812 Reorder the terms: 6 + k = 7.071067812 Solving 6 + k = 7.071067812 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 = 7.071067812 + -6 Combine like terms: 6 + -6 = 0 0 + k = 7.071067812 + -6 k = 7.071067812 + -6 Combine like terms: 7.071067812 + -6 = 1.071067812 k = 1.071067812 Simplifying k = 1.071067812Subproblem 2
k + 6 = -7.071067812 Simplifying k + 6 = -7.071067812 Reorder the terms: 6 + k = -7.071067812 Solving 6 + k = -7.071067812 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 = -7.071067812 + -6 Combine like terms: 6 + -6 = 0 0 + k = -7.071067812 + -6 k = -7.071067812 + -6 Combine like terms: -7.071067812 + -6 = -13.071067812 k = -13.071067812 Simplifying k = -13.071067812Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.071067812, -13.071067812}
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