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Simplifying 0.5k2 + 5k + 12.5 = 0 Reorder the terms: 12.5 + 5k + 0.5k2 = 0 Solving 12.5 + 5k + 0.5k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 25 + 10k + k2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + 10k + -25 + k2 = 0 + -25 Reorder the terms: 25 + -25 + 10k + k2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 10k + k2 = 0 + -25 10k + k2 = 0 + -25 Combine like terms: 0 + -25 = -25 10k + k2 = -25 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 = -25 + 25 Reorder the terms: 25 + 10k + k2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + 10k + k2 = 0 Factor a perfect square on the left side: (k + 5)(k + 5) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (k + 5) equal to 0 and 0.Subproblem 1
k + 5 = 0 Simplifying k + 5 = 0 Reorder the terms: 5 + k = 0 Solving 5 + k = 0 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 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + k = 0 + -5 k = 0 + -5 Combine like terms: 0 + -5 = -5 k = -5 Simplifying k = -5Subproblem 2
k + 5 = 0 Simplifying k + 5 = 0 Reorder the terms: 5 + k = 0 Solving 5 + k = 0 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 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + k = 0 + -5 k = 0 + -5 Combine like terms: 0 + -5 = -5 k = -5 Simplifying k = -5Solution
The solution to the problem is based on the solutions from the subproblems. k = {-5, -5}
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