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Simplifying 10k2 + 200k + 937.5 = 0 Reorder the terms: 937.5 + 200k + 10k2 = 0 Solving 937.5 + 200k + 10k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 93.75 + 20k + k2 = 0 Move the constant term to the right: Add '-93.75' to each side of the equation. 93.75 + 20k + -93.75 + k2 = 0 + -93.75 Reorder the terms: 93.75 + -93.75 + 20k + k2 = 0 + -93.75 Combine like terms: 93.75 + -93.75 = 0.00 0.00 + 20k + k2 = 0 + -93.75 20k + k2 = 0 + -93.75 Combine like terms: 0 + -93.75 = -93.75 20k + k2 = -93.75 The k term is 20k. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20k + 100 + k2 = -93.75 + 100 Reorder the terms: 100 + 20k + k2 = -93.75 + 100 Combine like terms: -93.75 + 100 = 6.25 100 + 20k + k2 = 6.25 Factor a perfect square on the left side: (k + 10)(k + 10) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (k + 10) equal to 2.5 and -2.5.Subproblem 1
k + 10 = 2.5 Simplifying k + 10 = 2.5 Reorder the terms: 10 + k = 2.5 Solving 10 + k = 2.5 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + k = 2.5 + -10 Combine like terms: 10 + -10 = 0 0 + k = 2.5 + -10 k = 2.5 + -10 Combine like terms: 2.5 + -10 = -7.5 k = -7.5 Simplifying k = -7.5Subproblem 2
k + 10 = -2.5 Simplifying k + 10 = -2.5 Reorder the terms: 10 + k = -2.5 Solving 10 + k = -2.5 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + k = -2.5 + -10 Combine like terms: 10 + -10 = 0 0 + k = -2.5 + -10 k = -2.5 + -10 Combine like terms: -2.5 + -10 = -12.5 k = -12.5 Simplifying k = -12.5Solution
The solution to the problem is based on the solutions from the subproblems. k = {-7.5, -12.5}
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