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Simplifying 0 = k2 + -28k + 40 Reorder the terms: 0 = 40 + -28k + k2 Solving 0 = 40 + -28k + k2 Solving for variable 'k'. Combine like terms: 0 + -40 = -40 -40 + 28k + -1k2 = 40 + -28k + k2 + -40 + 28k + -1k2 Reorder the terms: -40 + 28k + -1k2 = 40 + -40 + -28k + 28k + k2 + -1k2 Combine like terms: 40 + -40 = 0 -40 + 28k + -1k2 = 0 + -28k + 28k + k2 + -1k2 -40 + 28k + -1k2 = -28k + 28k + k2 + -1k2 Combine like terms: -28k + 28k = 0 -40 + 28k + -1k2 = 0 + k2 + -1k2 -40 + 28k + -1k2 = k2 + -1k2 Combine like terms: k2 + -1k2 = 0 -40 + 28k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -28k + k2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -28k + -40 + k2 = 0 + -40 Reorder the terms: 40 + -40 + -28k + k2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -28k + k2 = 0 + -40 -28k + k2 = 0 + -40 Combine like terms: 0 + -40 = -40 -28k + k2 = -40 The k term is -28k. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28k + 196 + k2 = -40 + 196 Reorder the terms: 196 + -28k + k2 = -40 + 196 Combine like terms: -40 + 196 = 156 196 + -28k + k2 = 156 Factor a perfect square on the left side: (k + -14)(k + -14) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (k + -14) equal to 12.489995997 and -12.489995997.Subproblem 1
k + -14 = 12.489995997 Simplifying k + -14 = 12.489995997 Reorder the terms: -14 + k = 12.489995997 Solving -14 + k = 12.489995997 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + k = 12.489995997 + 14 Combine like terms: -14 + 14 = 0 0 + k = 12.489995997 + 14 k = 12.489995997 + 14 Combine like terms: 12.489995997 + 14 = 26.489995997 k = 26.489995997 Simplifying k = 26.489995997Subproblem 2
k + -14 = -12.489995997 Simplifying k + -14 = -12.489995997 Reorder the terms: -14 + k = -12.489995997 Solving -14 + k = -12.489995997 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + k = -12.489995997 + 14 Combine like terms: -14 + 14 = 0 0 + k = -12.489995997 + 14 k = -12.489995997 + 14 Combine like terms: -12.489995997 + 14 = 1.510004003 k = 1.510004003 Simplifying k = 1.510004003Solution
The solution to the problem is based on the solutions from the subproblems. k = {26.489995997, 1.510004003}
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