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Simplifying k2 + -14k + 21 = 0 Reorder the terms: 21 + -14k + k2 = 0 Solving 21 + -14k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -14k + -21 + k2 = 0 + -21 Reorder the terms: 21 + -21 + -14k + k2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -14k + k2 = 0 + -21 -14k + k2 = 0 + -21 Combine like terms: 0 + -21 = -21 -14k + k2 = -21 The k term is -14k. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14k + 49 + k2 = -21 + 49 Reorder the terms: 49 + -14k + k2 = -21 + 49 Combine like terms: -21 + 49 = 28 49 + -14k + k2 = 28 Factor a perfect square on the left side: (k + -7)(k + -7) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (k + -7) equal to 5.291502622 and -5.291502622.Subproblem 1
k + -7 = 5.291502622 Simplifying k + -7 = 5.291502622 Reorder the terms: -7 + k = 5.291502622 Solving -7 + k = 5.291502622 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + k = 5.291502622 + 7 Combine like terms: -7 + 7 = 0 0 + k = 5.291502622 + 7 k = 5.291502622 + 7 Combine like terms: 5.291502622 + 7 = 12.291502622 k = 12.291502622 Simplifying k = 12.291502622Subproblem 2
k + -7 = -5.291502622 Simplifying k + -7 = -5.291502622 Reorder the terms: -7 + k = -5.291502622 Solving -7 + k = -5.291502622 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + k = -5.291502622 + 7 Combine like terms: -7 + 7 = 0 0 + k = -5.291502622 + 7 k = -5.291502622 + 7 Combine like terms: -5.291502622 + 7 = 1.708497378 k = 1.708497378 Simplifying k = 1.708497378Solution
The solution to the problem is based on the solutions from the subproblems. k = {12.291502622, 1.708497378}
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