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Simplifying k2 + -2k + -7 = 0 Reorder the terms: -7 + -2k + k2 = 0 Solving -7 + -2k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -2k + 7 + k2 = 0 + 7 Reorder the terms: -7 + 7 + -2k + k2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2k + k2 = 0 + 7 -2k + k2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2k + k2 = 7 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 = 7 + 1 Reorder the terms: 1 + -2k + k2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + -2k + k2 = 8 Factor a perfect square on the left side: (k + -1)(k + -1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (k + -1) equal to 2.828427125 and -2.828427125.Subproblem 1
k + -1 = 2.828427125 Simplifying k + -1 = 2.828427125 Reorder the terms: -1 + k = 2.828427125 Solving -1 + k = 2.828427125 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 = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + k = 2.828427125 + 1 k = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 k = 3.828427125 Simplifying k = 3.828427125Subproblem 2
k + -1 = -2.828427125 Simplifying k + -1 = -2.828427125 Reorder the terms: -1 + k = -2.828427125 Solving -1 + k = -2.828427125 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 = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + k = -2.828427125 + 1 k = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 k = -1.828427125 Simplifying k = -1.828427125Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.828427125, -1.828427125}
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