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Simplifying k2 + -1k + -7 = 0 Reorder the terms: -7 + -1k + k2 = 0 Solving -7 + -1k + 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 + -1k + 7 + k2 = 0 + 7 Reorder the terms: -7 + 7 + -1k + k2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1k + k2 = 0 + 7 -1k + k2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1k + k2 = 7 The k term is -1k. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1k + 0.25 + k2 = 7 + 0.25 Reorder the terms: 0.25 + -1k + k2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 0.25 + -1k + k2 = 7.25 Factor a perfect square on the left side: (k + -0.5)(k + -0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (k + -0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
k + -0.5 = 2.692582404 Simplifying k + -0.5 = 2.692582404 Reorder the terms: -0.5 + k = 2.692582404 Solving -0.5 + k = 2.692582404 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + k = 2.692582404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + k = 2.692582404 + 0.5 k = 2.692582404 + 0.5 Combine like terms: 2.692582404 + 0.5 = 3.192582404 k = 3.192582404 Simplifying k = 3.192582404Subproblem 2
k + -0.5 = -2.692582404 Simplifying k + -0.5 = -2.692582404 Reorder the terms: -0.5 + k = -2.692582404 Solving -0.5 + k = -2.692582404 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + k = -2.692582404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + k = -2.692582404 + 0.5 k = -2.692582404 + 0.5 Combine like terms: -2.692582404 + 0.5 = -2.192582404 k = -2.192582404 Simplifying k = -2.192582404Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.192582404, -2.192582404}
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