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Simplifying k2 + 10k + -27 = 0 Reorder the terms: -27 + 10k + k2 = 0 Solving -27 + 10k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 10k + 27 + k2 = 0 + 27 Reorder the terms: -27 + 27 + 10k + k2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 10k + k2 = 0 + 27 10k + k2 = 0 + 27 Combine like terms: 0 + 27 = 27 10k + k2 = 27 The k term is 10k. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10k + 25 + k2 = 27 + 25 Reorder the terms: 25 + 10k + k2 = 27 + 25 Combine like terms: 27 + 25 = 52 25 + 10k + k2 = 52 Factor a perfect square on the left side: (k + 5)(k + 5) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (k + 5) equal to 7.211102551 and -7.211102551.Subproblem 1
k + 5 = 7.211102551 Simplifying k + 5 = 7.211102551 Reorder the terms: 5 + k = 7.211102551 Solving 5 + k = 7.211102551 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + k = 7.211102551 + -5 Combine like terms: 5 + -5 = 0 0 + k = 7.211102551 + -5 k = 7.211102551 + -5 Combine like terms: 7.211102551 + -5 = 2.211102551 k = 2.211102551 Simplifying k = 2.211102551Subproblem 2
k + 5 = -7.211102551 Simplifying k + 5 = -7.211102551 Reorder the terms: 5 + k = -7.211102551 Solving 5 + k = -7.211102551 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + k = -7.211102551 + -5 Combine like terms: 5 + -5 = 0 0 + k = -7.211102551 + -5 k = -7.211102551 + -5 Combine like terms: -7.211102551 + -5 = -12.211102551 k = -12.211102551 Simplifying k = -12.211102551Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.211102551, -12.211102551}
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