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Simplifying k2 + -14k + -3 = 0 Reorder the terms: -3 + -14k + k2 = 0 Solving -3 + -14k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -14k + 3 + k2 = 0 + 3 Reorder the terms: -3 + 3 + -14k + k2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -14k + k2 = 0 + 3 -14k + k2 = 0 + 3 Combine like terms: 0 + 3 = 3 -14k + k2 = 3 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 = 3 + 49 Reorder the terms: 49 + -14k + k2 = 3 + 49 Combine like terms: 3 + 49 = 52 49 + -14k + k2 = 52 Factor a perfect square on the left side: (k + -7)(k + -7) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (k + -7) equal to 7.211102551 and -7.211102551.Subproblem 1
k + -7 = 7.211102551 Simplifying k + -7 = 7.211102551 Reorder the terms: -7 + k = 7.211102551 Solving -7 + k = 7.211102551 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 = 7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + k = 7.211102551 + 7 k = 7.211102551 + 7 Combine like terms: 7.211102551 + 7 = 14.211102551 k = 14.211102551 Simplifying k = 14.211102551Subproblem 2
k + -7 = -7.211102551 Simplifying k + -7 = -7.211102551 Reorder the terms: -7 + k = -7.211102551 Solving -7 + k = -7.211102551 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 = -7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + k = -7.211102551 + 7 k = -7.211102551 + 7 Combine like terms: -7.211102551 + 7 = -0.211102551 k = -0.211102551 Simplifying k = -0.211102551Solution
The solution to the problem is based on the solutions from the subproblems. k = {14.211102551, -0.211102551}
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