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Simplifying 35.4 + 0.025k2 = 12.7k Solving 35.4 + 0.025k2 = 12.7k Solving for variable 'k'. Reorder the terms: 35.4 + -12.7k + 0.025k2 = 12.7k + -12.7k Combine like terms: 12.7k + -12.7k = 0.0 35.4 + -12.7k + 0.025k2 = 0.0 Begin completing the square. Divide all terms by 0.025 the coefficient of the squared term: Divide each side by '0.025'. 1416 + -508k + k2 = 0 Move the constant term to the right: Add '-1416' to each side of the equation. 1416 + -508k + -1416 + k2 = 0 + -1416 Reorder the terms: 1416 + -1416 + -508k + k2 = 0 + -1416 Combine like terms: 1416 + -1416 = 0 0 + -508k + k2 = 0 + -1416 -508k + k2 = 0 + -1416 Combine like terms: 0 + -1416 = -1416 -508k + k2 = -1416 The k term is -508k. Take half its coefficient (-254). Square it (64516) and add it to both sides. Add '64516' to each side of the equation. -508k + 64516 + k2 = -1416 + 64516 Reorder the terms: 64516 + -508k + k2 = -1416 + 64516 Combine like terms: -1416 + 64516 = 63100 64516 + -508k + k2 = 63100 Factor a perfect square on the left side: (k + -254)(k + -254) = 63100 Calculate the square root of the right side: 251.197133742 Break this problem into two subproblems by setting (k + -254) equal to 251.197133742 and -251.197133742.Subproblem 1
k + -254 = 251.197133742 Simplifying k + -254 = 251.197133742 Reorder the terms: -254 + k = 251.197133742 Solving -254 + k = 251.197133742 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '254' to each side of the equation. -254 + 254 + k = 251.197133742 + 254 Combine like terms: -254 + 254 = 0 0 + k = 251.197133742 + 254 k = 251.197133742 + 254 Combine like terms: 251.197133742 + 254 = 505.197133742 k = 505.197133742 Simplifying k = 505.197133742Subproblem 2
k + -254 = -251.197133742 Simplifying k + -254 = -251.197133742 Reorder the terms: -254 + k = -251.197133742 Solving -254 + k = -251.197133742 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '254' to each side of the equation. -254 + 254 + k = -251.197133742 + 254 Combine like terms: -254 + 254 = 0 0 + k = -251.197133742 + 254 k = -251.197133742 + 254 Combine like terms: -251.197133742 + 254 = 2.802866258 k = 2.802866258 Simplifying k = 2.802866258Solution
The solution to the problem is based on the solutions from the subproblems. k = {505.197133742, 2.802866258}
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