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Simplifying k2 + 10k + -5 = 0 Reorder the terms: -5 + 10k + k2 = 0 Solving -5 + 10k + 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 + 10k + 5 + k2 = 0 + 5 Reorder the terms: -5 + 5 + 10k + k2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 10k + k2 = 0 + 5 10k + k2 = 0 + 5 Combine like terms: 0 + 5 = 5 10k + k2 = 5 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 = 5 + 25 Reorder the terms: 25 + 10k + k2 = 5 + 25 Combine like terms: 5 + 25 = 30 25 + 10k + k2 = 30 Factor a perfect square on the left side: (k + 5)(k + 5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (k + 5) equal to 5.477225575 and -5.477225575.Subproblem 1
k + 5 = 5.477225575 Simplifying k + 5 = 5.477225575 Reorder the terms: 5 + k = 5.477225575 Solving 5 + k = 5.477225575 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 = 5.477225575 + -5 Combine like terms: 5 + -5 = 0 0 + k = 5.477225575 + -5 k = 5.477225575 + -5 Combine like terms: 5.477225575 + -5 = 0.477225575 k = 0.477225575 Simplifying k = 0.477225575Subproblem 2
k + 5 = -5.477225575 Simplifying k + 5 = -5.477225575 Reorder the terms: 5 + k = -5.477225575 Solving 5 + k = -5.477225575 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 = -5.477225575 + -5 Combine like terms: 5 + -5 = 0 0 + k = -5.477225575 + -5 k = -5.477225575 + -5 Combine like terms: -5.477225575 + -5 = -10.477225575 k = -10.477225575 Simplifying k = -10.477225575Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.477225575, -10.477225575}
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