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Simplifying k2 + -8k + 13 = 0 Reorder the terms: 13 + -8k + k2 = 0 Solving 13 + -8k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8k + -13 + k2 = 0 + -13 Reorder the terms: 13 + -13 + -8k + k2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8k + k2 = 0 + -13 -8k + k2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8k + k2 = -13 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 = -13 + 16 Reorder the terms: 16 + -8k + k2 = -13 + 16 Combine like terms: -13 + 16 = 3 16 + -8k + k2 = 3 Factor a perfect square on the left side: (k + -4)(k + -4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (k + -4) equal to 1.732050808 and -1.732050808.Subproblem 1
k + -4 = 1.732050808 Simplifying k + -4 = 1.732050808 Reorder the terms: -4 + k = 1.732050808 Solving -4 + k = 1.732050808 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 = 1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + k = 1.732050808 + 4 k = 1.732050808 + 4 Combine like terms: 1.732050808 + 4 = 5.732050808 k = 5.732050808 Simplifying k = 5.732050808Subproblem 2
k + -4 = -1.732050808 Simplifying k + -4 = -1.732050808 Reorder the terms: -4 + k = -1.732050808 Solving -4 + k = -1.732050808 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 = -1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + k = -1.732050808 + 4 k = -1.732050808 + 4 Combine like terms: -1.732050808 + 4 = 2.267949192 k = 2.267949192 Simplifying k = 2.267949192Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.732050808, 2.267949192}
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