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Simplifying k2 + -8k = 8 Reorder the terms: -8k + k2 = 8 Solving -8k + k2 = 8 Solving for variable 'k'. Reorder the terms: -8 + -8k + k2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -8k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -8k + 8 + k2 = 0 + 8 Reorder the terms: -8 + 8 + -8k + k2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -8k + k2 = 0 + 8 -8k + k2 = 0 + 8 Combine like terms: 0 + 8 = 8 -8k + k2 = 8 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 = 8 + 16 Reorder the terms: 16 + -8k + k2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + -8k + k2 = 24 Factor a perfect square on the left side: (k + -4)(k + -4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (k + -4) equal to 4.898979486 and -4.898979486.Subproblem 1
k + -4 = 4.898979486 Simplifying k + -4 = 4.898979486 Reorder the terms: -4 + k = 4.898979486 Solving -4 + k = 4.898979486 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 = 4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + k = 4.898979486 + 4 k = 4.898979486 + 4 Combine like terms: 4.898979486 + 4 = 8.898979486 k = 8.898979486 Simplifying k = 8.898979486Subproblem 2
k + -4 = -4.898979486 Simplifying k + -4 = -4.898979486 Reorder the terms: -4 + k = -4.898979486 Solving -4 + k = -4.898979486 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 = -4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + k = -4.898979486 + 4 k = -4.898979486 + 4 Combine like terms: -4.898979486 + 4 = -0.898979486 k = -0.898979486 Simplifying k = -0.898979486Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.898979486, -0.898979486}
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