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Simplifying 5k2 + -6k + -34 = 0 Reorder the terms: -34 + -6k + 5k2 = 0 Solving -34 + -6k + 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'. -6.8 + -1.2k + k2 = 0 Move the constant term to the right: Add '6.8' to each side of the equation. -6.8 + -1.2k + 6.8 + k2 = 0 + 6.8 Reorder the terms: -6.8 + 6.8 + -1.2k + k2 = 0 + 6.8 Combine like terms: -6.8 + 6.8 = 0.0 0.0 + -1.2k + k2 = 0 + 6.8 -1.2k + k2 = 0 + 6.8 Combine like terms: 0 + 6.8 = 6.8 -1.2k + k2 = 6.8 The k term is -1.2k. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2k + 0.36 + k2 = 6.8 + 0.36 Reorder the terms: 0.36 + -1.2k + k2 = 6.8 + 0.36 Combine like terms: 6.8 + 0.36 = 7.16 0.36 + -1.2k + k2 = 7.16 Factor a perfect square on the left side: (k + -0.6)(k + -0.6) = 7.16 Calculate the square root of the right side: 2.675817632 Break this problem into two subproblems by setting (k + -0.6) equal to 2.675817632 and -2.675817632.Subproblem 1
k + -0.6 = 2.675817632 Simplifying k + -0.6 = 2.675817632 Reorder the terms: -0.6 + k = 2.675817632 Solving -0.6 + k = 2.675817632 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + k = 2.675817632 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + k = 2.675817632 + 0.6 k = 2.675817632 + 0.6 Combine like terms: 2.675817632 + 0.6 = 3.275817632 k = 3.275817632 Simplifying k = 3.275817632Subproblem 2
k + -0.6 = -2.675817632 Simplifying k + -0.6 = -2.675817632 Reorder the terms: -0.6 + k = -2.675817632 Solving -0.6 + k = -2.675817632 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + k = -2.675817632 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + k = -2.675817632 + 0.6 k = -2.675817632 + 0.6 Combine like terms: -2.675817632 + 0.6 = -2.075817632 k = -2.075817632 Simplifying k = -2.075817632Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.275817632, -2.075817632}
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