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Simplifying 4k2 + -36k + -36 = 0 Reorder the terms: -36 + -36k + 4k2 = 0 Solving -36 + -36k + 4k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -9k + k2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -9k + k2)' equal to zero and attempt to solve: Simplifying -9 + -9k + k2 = 0 Solving -9 + -9k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -9k + 9 + k2 = 0 + 9 Reorder the terms: -9 + 9 + -9k + k2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -9k + k2 = 0 + 9 -9k + k2 = 0 + 9 Combine like terms: 0 + 9 = 9 -9k + k2 = 9 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 = 9 + 20.25 Reorder the terms: 20.25 + -9k + k2 = 9 + 20.25 Combine like terms: 9 + 20.25 = 29.25 20.25 + -9k + k2 = 29.25 Factor a perfect square on the left side: (k + -4.5)(k + -4.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (k + -4.5) equal to 5.408326913 and -5.408326913.Subproblem 1
k + -4.5 = 5.408326913 Simplifying k + -4.5 = 5.408326913 Reorder the terms: -4.5 + k = 5.408326913 Solving -4.5 + k = 5.408326913 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 = 5.408326913 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + k = 5.408326913 + 4.5 k = 5.408326913 + 4.5 Combine like terms: 5.408326913 + 4.5 = 9.908326913 k = 9.908326913 Simplifying k = 9.908326913Subproblem 2
k + -4.5 = -5.408326913 Simplifying k + -4.5 = -5.408326913 Reorder the terms: -4.5 + k = -5.408326913 Solving -4.5 + k = -5.408326913 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 = -5.408326913 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + k = -5.408326913 + 4.5 k = -5.408326913 + 4.5 Combine like terms: -5.408326913 + 4.5 = -0.908326913 k = -0.908326913 Simplifying k = -0.908326913Solution
The solution to the problem is based on the solutions from the subproblems. k = {9.908326913, -0.908326913}Solution
k = {9.908326913, -0.908326913}
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