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Simplifying 5k2 + -20k + -64 = 0 Reorder the terms: -64 + -20k + 5k2 = 0 Solving -64 + -20k + 5k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.8 + -4k + k2 = 0 Move the constant term to the right: Add '12.8' to each side of the equation. -12.8 + -4k + 12.8 + k2 = 0 + 12.8 Reorder the terms: -12.8 + 12.8 + -4k + k2 = 0 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + -4k + k2 = 0 + 12.8 -4k + k2 = 0 + 12.8 Combine like terms: 0 + 12.8 = 12.8 -4k + k2 = 12.8 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 = 12.8 + 4 Reorder the terms: 4 + -4k + k2 = 12.8 + 4 Combine like terms: 12.8 + 4 = 16.8 4 + -4k + k2 = 16.8 Factor a perfect square on the left side: (k + -2)(k + -2) = 16.8 Calculate the square root of the right side: 4.098780306 Break this problem into two subproblems by setting (k + -2) equal to 4.098780306 and -4.098780306.Subproblem 1
k + -2 = 4.098780306 Simplifying k + -2 = 4.098780306 Reorder the terms: -2 + k = 4.098780306 Solving -2 + k = 4.098780306 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 = 4.098780306 + 2 Combine like terms: -2 + 2 = 0 0 + k = 4.098780306 + 2 k = 4.098780306 + 2 Combine like terms: 4.098780306 + 2 = 6.098780306 k = 6.098780306 Simplifying k = 6.098780306Subproblem 2
k + -2 = -4.098780306 Simplifying k + -2 = -4.098780306 Reorder the terms: -2 + k = -4.098780306 Solving -2 + k = -4.098780306 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 = -4.098780306 + 2 Combine like terms: -2 + 2 = 0 0 + k = -4.098780306 + 2 k = -4.098780306 + 2 Combine like terms: -4.098780306 + 2 = -2.098780306 k = -2.098780306 Simplifying k = -2.098780306Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.098780306, -2.098780306}
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