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Simplifying (2k + -3)(2k + -3) = 44 Reorder the terms: (-3 + 2k)(2k + -3) = 44 Reorder the terms: (-3 + 2k)(-3 + 2k) = 44 Multiply (-3 + 2k) * (-3 + 2k) (-3(-3 + 2k) + 2k * (-3 + 2k)) = 44 ((-3 * -3 + 2k * -3) + 2k * (-3 + 2k)) = 44 ((9 + -6k) + 2k * (-3 + 2k)) = 44 (9 + -6k + (-3 * 2k + 2k * 2k)) = 44 (9 + -6k + (-6k + 4k2)) = 44 Combine like terms: -6k + -6k = -12k (9 + -12k + 4k2) = 44 Solving 9 + -12k + 4k2 = 44 Solving for variable 'k'. Reorder the terms: 9 + -44 + -12k + 4k2 = 44 + -44 Combine like terms: 9 + -44 = -35 -35 + -12k + 4k2 = 44 + -44 Combine like terms: 44 + -44 = 0 -35 + -12k + 4k2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + -3k + k2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -3k + 8.75 + k2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -3k + k2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -3k + k2 = 0 + 8.75 -3k + k2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -3k + k2 = 8.75 The k term is -3k. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3k + 2.25 + k2 = 8.75 + 2.25 Reorder the terms: 2.25 + -3k + k2 = 8.75 + 2.25 Combine like terms: 8.75 + 2.25 = 11 2.25 + -3k + k2 = 11 Factor a perfect square on the left side: (k + -1.5)(k + -1.5) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (k + -1.5) equal to 3.31662479 and -3.31662479.Subproblem 1
k + -1.5 = 3.31662479 Simplifying k + -1.5 = 3.31662479 Reorder the terms: -1.5 + k = 3.31662479 Solving -1.5 + k = 3.31662479 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + k = 3.31662479 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = 3.31662479 + 1.5 k = 3.31662479 + 1.5 Combine like terms: 3.31662479 + 1.5 = 4.81662479 k = 4.81662479 Simplifying k = 4.81662479Subproblem 2
k + -1.5 = -3.31662479 Simplifying k + -1.5 = -3.31662479 Reorder the terms: -1.5 + k = -3.31662479 Solving -1.5 + k = -3.31662479 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + k = -3.31662479 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + k = -3.31662479 + 1.5 k = -3.31662479 + 1.5 Combine like terms: -3.31662479 + 1.5 = -1.81662479 k = -1.81662479 Simplifying k = -1.81662479Solution
The solution to the problem is based on the solutions from the subproblems. k = {4.81662479, -1.81662479}
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