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Simplifying k2 + 14k + 5 = 0 Reorder the terms: 5 + 14k + k2 = 0 Solving 5 + 14k + k2 = 0 Solving for variable 'k'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 14k + -5 + k2 = 0 + -5 Reorder the terms: 5 + -5 + 14k + k2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 14k + k2 = 0 + -5 14k + k2 = 0 + -5 Combine like terms: 0 + -5 = -5 14k + k2 = -5 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 = -5 + 49 Reorder the terms: 49 + 14k + k2 = -5 + 49 Combine like terms: -5 + 49 = 44 49 + 14k + k2 = 44 Factor a perfect square on the left side: (k + 7)(k + 7) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (k + 7) equal to 6.633249581 and -6.633249581.Subproblem 1
k + 7 = 6.633249581 Simplifying k + 7 = 6.633249581 Reorder the terms: 7 + k = 6.633249581 Solving 7 + k = 6.633249581 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 = 6.633249581 + -7 Combine like terms: 7 + -7 = 0 0 + k = 6.633249581 + -7 k = 6.633249581 + -7 Combine like terms: 6.633249581 + -7 = -0.366750419 k = -0.366750419 Simplifying k = -0.366750419Subproblem 2
k + 7 = -6.633249581 Simplifying k + 7 = -6.633249581 Reorder the terms: 7 + k = -6.633249581 Solving 7 + k = -6.633249581 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 = -6.633249581 + -7 Combine like terms: 7 + -7 = 0 0 + k = -6.633249581 + -7 k = -6.633249581 + -7 Combine like terms: -6.633249581 + -7 = -13.633249581 k = -13.633249581 Simplifying k = -13.633249581Solution
The solution to the problem is based on the solutions from the subproblems. k = {-0.366750419, -13.633249581}
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