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Simplifying -1k2 + 10k + 25 = -5 Reorder the terms: 25 + 10k + -1k2 = -5 Solving 25 + 10k + -1k2 = -5 Solving for variable 'k'. Reorder the terms: 25 + 5 + 10k + -1k2 = -5 + 5 Combine like terms: 25 + 5 = 30 30 + 10k + -1k2 = -5 + 5 Combine like terms: -5 + 5 = 0 30 + 10k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + -10k + k2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -10k + 30 + k2 = 0 + 30 Reorder the terms: -30 + 30 + -10k + k2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -10k + k2 = 0 + 30 -10k + k2 = 0 + 30 Combine like terms: 0 + 30 = 30 -10k + k2 = 30 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 = 30 + 25 Reorder the terms: 25 + -10k + k2 = 30 + 25 Combine like terms: 30 + 25 = 55 25 + -10k + k2 = 55 Factor a perfect square on the left side: (k + -5)(k + -5) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (k + -5) equal to 7.416198487 and -7.416198487.Subproblem 1
k + -5 = 7.416198487 Simplifying k + -5 = 7.416198487 Reorder the terms: -5 + k = 7.416198487 Solving -5 + k = 7.416198487 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 = 7.416198487 + 5 Combine like terms: -5 + 5 = 0 0 + k = 7.416198487 + 5 k = 7.416198487 + 5 Combine like terms: 7.416198487 + 5 = 12.416198487 k = 12.416198487 Simplifying k = 12.416198487Subproblem 2
k + -5 = -7.416198487 Simplifying k + -5 = -7.416198487 Reorder the terms: -5 + k = -7.416198487 Solving -5 + k = -7.416198487 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 = -7.416198487 + 5 Combine like terms: -5 + 5 = 0 0 + k = -7.416198487 + 5 k = -7.416198487 + 5 Combine like terms: -7.416198487 + 5 = -2.416198487 k = -2.416198487 Simplifying k = -2.416198487Solution
The solution to the problem is based on the solutions from the subproblems. k = {12.416198487, -2.416198487}
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