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Simplifying 5k2 + -4k = 13 Reorder the terms: -4k + 5k2 = 13 Solving -4k + 5k2 = 13 Solving for variable 'k'. Reorder the terms: -13 + -4k + 5k2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -4k + 5k2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + -0.8k + k2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -0.8k + 2.6 + k2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -0.8k + k2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -0.8k + k2 = 0 + 2.6 -0.8k + k2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -0.8k + k2 = 2.6 The k term is -0.8k. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8k + 0.16 + k2 = 2.6 + 0.16 Reorder the terms: 0.16 + -0.8k + k2 = 2.6 + 0.16 Combine like terms: 2.6 + 0.16 = 2.76 0.16 + -0.8k + k2 = 2.76 Factor a perfect square on the left side: (k + -0.4)(k + -0.4) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (k + -0.4) equal to 1.661324773 and -1.661324773.Subproblem 1
k + -0.4 = 1.661324773 Simplifying k + -0.4 = 1.661324773 Reorder the terms: -0.4 + k = 1.661324773 Solving -0.4 + k = 1.661324773 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + k = 1.661324773 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + k = 1.661324773 + 0.4 k = 1.661324773 + 0.4 Combine like terms: 1.661324773 + 0.4 = 2.061324773 k = 2.061324773 Simplifying k = 2.061324773Subproblem 2
k + -0.4 = -1.661324773 Simplifying k + -0.4 = -1.661324773 Reorder the terms: -0.4 + k = -1.661324773 Solving -0.4 + k = -1.661324773 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + k = -1.661324773 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + k = -1.661324773 + 0.4 k = -1.661324773 + 0.4 Combine like terms: -1.661324773 + 0.4 = -1.261324773 k = -1.261324773 Simplifying k = -1.261324773Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.061324773, -1.261324773}
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