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Simplifying 9k2 + 11k + -26 = 4k + -3 Reorder the terms: -26 + 11k + 9k2 = 4k + -3 Reorder the terms: -26 + 11k + 9k2 = -3 + 4k Solving -26 + 11k + 9k2 = -3 + 4k Solving for variable 'k'. Reorder the terms: -26 + 3 + 11k + -4k + 9k2 = -3 + 4k + 3 + -4k Combine like terms: -26 + 3 = -23 -23 + 11k + -4k + 9k2 = -3 + 4k + 3 + -4k Combine like terms: 11k + -4k = 7k -23 + 7k + 9k2 = -3 + 4k + 3 + -4k Reorder the terms: -23 + 7k + 9k2 = -3 + 3 + 4k + -4k Combine like terms: -3 + 3 = 0 -23 + 7k + 9k2 = 0 + 4k + -4k -23 + 7k + 9k2 = 4k + -4k Combine like terms: 4k + -4k = 0 -23 + 7k + 9k2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.555555556 + 0.7777777778k + k2 = 0 Move the constant term to the right: Add '2.555555556' to each side of the equation. -2.555555556 + 0.7777777778k + 2.555555556 + k2 = 0 + 2.555555556 Reorder the terms: -2.555555556 + 2.555555556 + 0.7777777778k + k2 = 0 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + 0.7777777778k + k2 = 0 + 2.555555556 0.7777777778k + k2 = 0 + 2.555555556 Combine like terms: 0 + 2.555555556 = 2.555555556 0.7777777778k + k2 = 2.555555556 The k term is 0.7777777778k. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778k + 0.1512345679 + k2 = 2.555555556 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778k + k2 = 2.555555556 + 0.1512345679 Combine like terms: 2.555555556 + 0.1512345679 = 2.7067901239 0.1512345679 + 0.7777777778k + k2 = 2.7067901239 Factor a perfect square on the left side: (k + 0.3888888889)(k + 0.3888888889) = 2.7067901239 Calculate the square root of the right side: 1.645232544 Break this problem into two subproblems by setting (k + 0.3888888889) equal to 1.645232544 and -1.645232544.Subproblem 1
k + 0.3888888889 = 1.645232544 Simplifying k + 0.3888888889 = 1.645232544 Reorder the terms: 0.3888888889 + k = 1.645232544 Solving 0.3888888889 + k = 1.645232544 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + k = 1.645232544 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + k = 1.645232544 + -0.3888888889 k = 1.645232544 + -0.3888888889 Combine like terms: 1.645232544 + -0.3888888889 = 1.2563436551 k = 1.2563436551 Simplifying k = 1.2563436551Subproblem 2
k + 0.3888888889 = -1.645232544 Simplifying k + 0.3888888889 = -1.645232544 Reorder the terms: 0.3888888889 + k = -1.645232544 Solving 0.3888888889 + k = -1.645232544 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + k = -1.645232544 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + k = -1.645232544 + -0.3888888889 k = -1.645232544 + -0.3888888889 Combine like terms: -1.645232544 + -0.3888888889 = -2.0341214329 k = -2.0341214329 Simplifying k = -2.0341214329Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.2563436551, -2.0341214329}
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