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Simplifying 2600 = k2 + -480k + 57600 Reorder the terms: 2600 = 57600 + -480k + k2 Solving 2600 = 57600 + -480k + k2 Solving for variable 'k'. Combine like terms: 2600 + -57600 = -55000 -55000 + 480k + -1k2 = 57600 + -480k + k2 + -57600 + 480k + -1k2 Reorder the terms: -55000 + 480k + -1k2 = 57600 + -57600 + -480k + 480k + k2 + -1k2 Combine like terms: 57600 + -57600 = 0 -55000 + 480k + -1k2 = 0 + -480k + 480k + k2 + -1k2 -55000 + 480k + -1k2 = -480k + 480k + k2 + -1k2 Combine like terms: -480k + 480k = 0 -55000 + 480k + -1k2 = 0 + k2 + -1k2 -55000 + 480k + -1k2 = k2 + -1k2 Combine like terms: k2 + -1k2 = 0 -55000 + 480k + -1k2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 55000 + -480k + k2 = 0 Move the constant term to the right: Add '-55000' to each side of the equation. 55000 + -480k + -55000 + k2 = 0 + -55000 Reorder the terms: 55000 + -55000 + -480k + k2 = 0 + -55000 Combine like terms: 55000 + -55000 = 0 0 + -480k + k2 = 0 + -55000 -480k + k2 = 0 + -55000 Combine like terms: 0 + -55000 = -55000 -480k + k2 = -55000 The k term is -480k. Take half its coefficient (-240). Square it (57600) and add it to both sides. Add '57600' to each side of the equation. -480k + 57600 + k2 = -55000 + 57600 Reorder the terms: 57600 + -480k + k2 = -55000 + 57600 Combine like terms: -55000 + 57600 = 2600 57600 + -480k + k2 = 2600 Factor a perfect square on the left side: (k + -240)(k + -240) = 2600 Calculate the square root of the right side: 50.990195136 Break this problem into two subproblems by setting (k + -240) equal to 50.990195136 and -50.990195136.Subproblem 1
k + -240 = 50.990195136 Simplifying k + -240 = 50.990195136 Reorder the terms: -240 + k = 50.990195136 Solving -240 + k = 50.990195136 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '240' to each side of the equation. -240 + 240 + k = 50.990195136 + 240 Combine like terms: -240 + 240 = 0 0 + k = 50.990195136 + 240 k = 50.990195136 + 240 Combine like terms: 50.990195136 + 240 = 290.990195136 k = 290.990195136 Simplifying k = 290.990195136Subproblem 2
k + -240 = -50.990195136 Simplifying k + -240 = -50.990195136 Reorder the terms: -240 + k = -50.990195136 Solving -240 + k = -50.990195136 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '240' to each side of the equation. -240 + 240 + k = -50.990195136 + 240 Combine like terms: -240 + 240 = 0 0 + k = -50.990195136 + 240 k = -50.990195136 + 240 Combine like terms: -50.990195136 + 240 = 189.009804864 k = 189.009804864 Simplifying k = 189.009804864Solution
The solution to the problem is based on the solutions from the subproblems. k = {290.990195136, 189.009804864}
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