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Simplifying 5k2 + -20k = 81 Reorder the terms: -20k + 5k2 = 81 Solving -20k + 5k2 = 81 Solving for variable 'k'. Reorder the terms: -81 + -20k + 5k2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + -20k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16.2 + -4k + k2 = 0 Move the constant term to the right: Add '16.2' to each side of the equation. -16.2 + -4k + 16.2 + k2 = 0 + 16.2 Reorder the terms: -16.2 + 16.2 + -4k + k2 = 0 + 16.2 Combine like terms: -16.2 + 16.2 = 0.0 0.0 + -4k + k2 = 0 + 16.2 -4k + k2 = 0 + 16.2 Combine like terms: 0 + 16.2 = 16.2 -4k + k2 = 16.2 The k term is -4k. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4k + 4 + k2 = 16.2 + 4 Reorder the terms: 4 + -4k + k2 = 16.2 + 4 Combine like terms: 16.2 + 4 = 20.2 4 + -4k + k2 = 20.2 Factor a perfect square on the left side: (k + -2)(k + -2) = 20.2 Calculate the square root of the right side: 4.494441011 Break this problem into two subproblems by setting (k + -2) equal to 4.494441011 and -4.494441011.Subproblem 1
k + -2 = 4.494441011 Simplifying k + -2 = 4.494441011 Reorder the terms: -2 + k = 4.494441011 Solving -2 + k = 4.494441011 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = 4.494441011 + 2 Combine like terms: -2 + 2 = 0 0 + k = 4.494441011 + 2 k = 4.494441011 + 2 Combine like terms: 4.494441011 + 2 = 6.494441011 k = 6.494441011 Simplifying k = 6.494441011Subproblem 2
k + -2 = -4.494441011 Simplifying k + -2 = -4.494441011 Reorder the terms: -2 + k = -4.494441011 Solving -2 + k = -4.494441011 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = -4.494441011 + 2 Combine like terms: -2 + 2 = 0 0 + k = -4.494441011 + 2 k = -4.494441011 + 2 Combine like terms: -4.494441011 + 2 = -2.494441011 k = -2.494441011 Simplifying k = -2.494441011Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.494441011, -2.494441011}
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