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Simplifying 4(k2 + 9k + 5) = 0 Reorder the terms: 4(5 + 9k + k2) = 0 (5 * 4 + 9k * 4 + k2 * 4) = 0 (20 + 36k + 4k2) = 0 Solving 20 + 36k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 9k + k2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 9k + k2)' equal to zero and attempt to solve: Simplifying 5 + 9k + k2 = 0 Solving 5 + 9k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 9k + -5 + k2 = 0 + -5 Reorder the terms: 5 + -5 + 9k + k2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9k + k2 = 0 + -5 9k + k2 = 0 + -5 Combine like terms: 0 + -5 = -5 9k + k2 = -5 The k term is 9k. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9k + 20.25 + k2 = -5 + 20.25 Reorder the terms: 20.25 + 9k + k2 = -5 + 20.25 Combine like terms: -5 + 20.25 = 15.25 20.25 + 9k + k2 = 15.25 Factor a perfect square on the left side: (k + 4.5)(k + 4.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (k + 4.5) equal to 3.905124838 and -3.905124838.Subproblem 1
k + 4.5 = 3.905124838 Simplifying k + 4.5 = 3.905124838 Reorder the terms: 4.5 + k = 3.905124838 Solving 4.5 + k = 3.905124838 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + k = 3.905124838 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = 3.905124838 + -4.5 k = 3.905124838 + -4.5 Combine like terms: 3.905124838 + -4.5 = -0.594875162 k = -0.594875162 Simplifying k = -0.594875162Subproblem 2
k + 4.5 = -3.905124838 Simplifying k + 4.5 = -3.905124838 Reorder the terms: 4.5 + k = -3.905124838 Solving 4.5 + k = -3.905124838 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + k = -3.905124838 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + k = -3.905124838 + -4.5 k = -3.905124838 + -4.5 Combine like terms: -3.905124838 + -4.5 = -8.405124838 k = -8.405124838 Simplifying k = -8.405124838Solution
The solution to the problem is based on the solutions from the subproblems. k = {-0.594875162, -8.405124838}Solution
k = {-0.594875162, -8.405124838}
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