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Simplifying 6k2 + -42k + -49 = 0 Reorder the terms: -49 + -42k + 6k2 = 0 Solving -49 + -42k + 6k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -8.166666667 + -7k + k2 = 0 Move the constant term to the right: Add '8.166666667' to each side of the equation. -8.166666667 + -7k + 8.166666667 + k2 = 0 + 8.166666667 Reorder the terms: -8.166666667 + 8.166666667 + -7k + k2 = 0 + 8.166666667 Combine like terms: -8.166666667 + 8.166666667 = 0.000000000 0.000000000 + -7k + k2 = 0 + 8.166666667 -7k + k2 = 0 + 8.166666667 Combine like terms: 0 + 8.166666667 = 8.166666667 -7k + k2 = 8.166666667 The k term is -7k. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7k + 12.25 + k2 = 8.166666667 + 12.25 Reorder the terms: 12.25 + -7k + k2 = 8.166666667 + 12.25 Combine like terms: 8.166666667 + 12.25 = 20.416666667 12.25 + -7k + k2 = 20.416666667 Factor a perfect square on the left side: (k + -3.5)(k + -3.5) = 20.416666667 Calculate the square root of the right side: 4.518480571 Break this problem into two subproblems by setting (k + -3.5) equal to 4.518480571 and -4.518480571.Subproblem 1
k + -3.5 = 4.518480571 Simplifying k + -3.5 = 4.518480571 Reorder the terms: -3.5 + k = 4.518480571 Solving -3.5 + k = 4.518480571 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + k = 4.518480571 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = 4.518480571 + 3.5 k = 4.518480571 + 3.5 Combine like terms: 4.518480571 + 3.5 = 8.018480571 k = 8.018480571 Simplifying k = 8.018480571Subproblem 2
k + -3.5 = -4.518480571 Simplifying k + -3.5 = -4.518480571 Reorder the terms: -3.5 + k = -4.518480571 Solving -3.5 + k = -4.518480571 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + k = -4.518480571 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = -4.518480571 + 3.5 k = -4.518480571 + 3.5 Combine like terms: -4.518480571 + 3.5 = -1.018480571 k = -1.018480571 Simplifying k = -1.018480571Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.018480571, -1.018480571}
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