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Simplifying 5k2 + -7k + -13 = 0 Reorder the terms: -13 + -7k + 5k2 = 0 Solving -13 + -7k + 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'. -2.6 + -1.4k + k2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -1.4k + 2.6 + k2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -1.4k + k2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -1.4k + k2 = 0 + 2.6 -1.4k + k2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -1.4k + k2 = 2.6 The k term is -1.4k. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4k + 0.49 + k2 = 2.6 + 0.49 Reorder the terms: 0.49 + -1.4k + k2 = 2.6 + 0.49 Combine like terms: 2.6 + 0.49 = 3.09 0.49 + -1.4k + k2 = 3.09 Factor a perfect square on the left side: (k + -0.7)(k + -0.7) = 3.09 Calculate the square root of the right side: 1.757839583 Break this problem into two subproblems by setting (k + -0.7) equal to 1.757839583 and -1.757839583.Subproblem 1
k + -0.7 = 1.757839583 Simplifying k + -0.7 = 1.757839583 Reorder the terms: -0.7 + k = 1.757839583 Solving -0.7 + k = 1.757839583 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + k = 1.757839583 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + k = 1.757839583 + 0.7 k = 1.757839583 + 0.7 Combine like terms: 1.757839583 + 0.7 = 2.457839583 k = 2.457839583 Simplifying k = 2.457839583Subproblem 2
k + -0.7 = -1.757839583 Simplifying k + -0.7 = -1.757839583 Reorder the terms: -0.7 + k = -1.757839583 Solving -0.7 + k = -1.757839583 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + k = -1.757839583 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + k = -1.757839583 + 0.7 k = -1.757839583 + 0.7 Combine like terms: -1.757839583 + 0.7 = -1.057839583 k = -1.057839583 Simplifying k = -1.057839583Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.457839583, -1.057839583}
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