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Simplifying k2 = -8k + 14 Reorder the terms: k2 = 14 + -8k Solving k2 = 14 + -8k Solving for variable 'k'. Reorder the terms: -14 + 8k + k2 = 14 + -8k + -14 + 8k Reorder the terms: -14 + 8k + k2 = 14 + -14 + -8k + 8k Combine like terms: 14 + -14 = 0 -14 + 8k + k2 = 0 + -8k + 8k -14 + 8k + k2 = -8k + 8k Combine like terms: -8k + 8k = 0 -14 + 8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 8k + 14 + k2 = 0 + 14 Reorder the terms: -14 + 14 + 8k + k2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 8k + k2 = 0 + 14 8k + k2 = 0 + 14 Combine like terms: 0 + 14 = 14 8k + k2 = 14 The k term is 8k. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8k + 16 + k2 = 14 + 16 Reorder the terms: 16 + 8k + k2 = 14 + 16 Combine like terms: 14 + 16 = 30 16 + 8k + k2 = 30 Factor a perfect square on the left side: (k + 4)(k + 4) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (k + 4) equal to 5.477225575 and -5.477225575.Subproblem 1
k + 4 = 5.477225575 Simplifying k + 4 = 5.477225575 Reorder the terms: 4 + k = 5.477225575 Solving 4 + k = 5.477225575 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + k = 5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + k = 5.477225575 + -4 k = 5.477225575 + -4 Combine like terms: 5.477225575 + -4 = 1.477225575 k = 1.477225575 Simplifying k = 1.477225575Subproblem 2
k + 4 = -5.477225575 Simplifying k + 4 = -5.477225575 Reorder the terms: 4 + k = -5.477225575 Solving 4 + k = -5.477225575 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + k = -5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + k = -5.477225575 + -4 k = -5.477225575 + -4 Combine like terms: -5.477225575 + -4 = -9.477225575 k = -9.477225575 Simplifying k = -9.477225575Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.477225575, -9.477225575}
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