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Simplifying 36k2 = 60k + 25 Reorder the terms: 36k2 = 25 + 60k Solving 36k2 = 25 + 60k Solving for variable 'k'. Reorder the terms: -25 + -60k + 36k2 = 25 + 60k + -25 + -60k Reorder the terms: -25 + -60k + 36k2 = 25 + -25 + 60k + -60k Combine like terms: 25 + -25 = 0 -25 + -60k + 36k2 = 0 + 60k + -60k -25 + -60k + 36k2 = 60k + -60k Combine like terms: 60k + -60k = 0 -25 + -60k + 36k2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.6944444444 + -1.666666667k + k2 = 0 Move the constant term to the right: Add '0.6944444444' to each side of the equation. -0.6944444444 + -1.666666667k + 0.6944444444 + k2 = 0 + 0.6944444444 Reorder the terms: -0.6944444444 + 0.6944444444 + -1.666666667k + k2 = 0 + 0.6944444444 Combine like terms: -0.6944444444 + 0.6944444444 = 0.0000000000 0.0000000000 + -1.666666667k + k2 = 0 + 0.6944444444 -1.666666667k + k2 = 0 + 0.6944444444 Combine like terms: 0 + 0.6944444444 = 0.6944444444 -1.666666667k + k2 = 0.6944444444 The k term is -1.666666667k. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667k + 0.6944444447 + k2 = 0.6944444444 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667k + k2 = 0.6944444444 + 0.6944444447 Combine like terms: 0.6944444444 + 0.6944444447 = 1.3888888891 0.6944444447 + -1.666666667k + k2 = 1.3888888891 Factor a perfect square on the left side: (k + -0.8333333335)(k + -0.8333333335) = 1.3888888891 Calculate the square root of the right side: 1.178511302 Break this problem into two subproblems by setting (k + -0.8333333335) equal to 1.178511302 and -1.178511302.Subproblem 1
k + -0.8333333335 = 1.178511302 Simplifying k + -0.8333333335 = 1.178511302 Reorder the terms: -0.8333333335 + k = 1.178511302 Solving -0.8333333335 + k = 1.178511302 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + k = 1.178511302 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + k = 1.178511302 + 0.8333333335 k = 1.178511302 + 0.8333333335 Combine like terms: 1.178511302 + 0.8333333335 = 2.0118446355 k = 2.0118446355 Simplifying k = 2.0118446355Subproblem 2
k + -0.8333333335 = -1.178511302 Simplifying k + -0.8333333335 = -1.178511302 Reorder the terms: -0.8333333335 + k = -1.178511302 Solving -0.8333333335 + k = -1.178511302 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + k = -1.178511302 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + k = -1.178511302 + 0.8333333335 k = -1.178511302 + 0.8333333335 Combine like terms: -1.178511302 + 0.8333333335 = -0.3451779685 k = -0.3451779685 Simplifying k = -0.3451779685Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.0118446355, -0.3451779685}
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