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Simplifying 2k2 + 6k + 4.5 = 0 Reorder the terms: 4.5 + 6k + 2k2 = 0 Solving 4.5 + 6k + 2k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.25 + 3k + k2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 3k + -2.25 + k2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 3k + k2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 3k + k2 = 0 + -2.25 3k + k2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 3k + k2 = -2.25 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 = -2.25 + 2.25 Reorder the terms: 2.25 + 3k + k2 = -2.25 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 2.25 + 3k + k2 = 0.00 Factor a perfect square on the left side: (k + 1.5)(k + 1.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (k + 1.5) equal to 0.00 and 0.00.Subproblem 1
k + 1.5 = 0.00 Simplifying k + 1.5 = 0.00 Reorder the terms: 1.5 + k = 0.00 Solving 1.5 + k = 0.00 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 = 0.00 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + k = 0.00 + -1.5 k = 0.00 + -1.5 Combine like terms: 0.00 + -1.5 = -1.5 k = -1.5 Simplifying k = -1.5Subproblem 2
k + 1.5 = 0.00 Simplifying k + 1.5 = 0.00 Reorder the terms: 1.5 + k = 0.00 Solving 1.5 + k = 0.00 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 = 0.00 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + k = 0.00 + -1.5 k = 0.00 + -1.5 Combine like terms: 0.00 + -1.5 = -1.5 k = -1.5 Simplifying k = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. k = {-1.5, -1.5}
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