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Simplifying k2 + -2k + -8 = 3 Reorder the terms: -8 + -2k + k2 = 3 Solving -8 + -2k + k2 = 3 Solving for variable 'k'. Reorder the terms: -8 + -3 + -2k + k2 = 3 + -3 Combine like terms: -8 + -3 = -11 -11 + -2k + k2 = 3 + -3 Combine like terms: 3 + -3 = 0 -11 + -2k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -2k + 11 + k2 = 0 + 11 Reorder the terms: -11 + 11 + -2k + k2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2k + k2 = 0 + 11 -2k + k2 = 0 + 11 Combine like terms: 0 + 11 = 11 -2k + k2 = 11 The k term is -2k. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2k + 1 + k2 = 11 + 1 Reorder the terms: 1 + -2k + k2 = 11 + 1 Combine like terms: 11 + 1 = 12 1 + -2k + k2 = 12 Factor a perfect square on the left side: (k + -1)(k + -1) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (k + -1) equal to 3.464101615 and -3.464101615.Subproblem 1
k + -1 = 3.464101615 Simplifying k + -1 = 3.464101615 Reorder the terms: -1 + k = 3.464101615 Solving -1 + k = 3.464101615 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + k = 3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + k = 3.464101615 + 1 k = 3.464101615 + 1 Combine like terms: 3.464101615 + 1 = 4.464101615 k = 4.464101615 Simplifying k = 4.464101615Subproblem 2
k + -1 = -3.464101615 Simplifying k + -1 = -3.464101615 Reorder the terms: -1 + k = -3.464101615 Solving -1 + k = -3.464101615 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + k = -3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + k = -3.464101615 + 1 k = -3.464101615 + 1 Combine like terms: -3.464101615 + 1 = -2.464101615 k = -2.464101615 Simplifying k = -2.464101615Solution
The solution to the problem is based on the solutions from the subproblems. k = {4.464101615, -2.464101615}
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