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Simplifying -4k2 + -88k = 108 Reorder the terms: -88k + -4k2 = 108 Solving -88k + -4k2 = 108 Solving for variable 'k'. Reorder the terms: -108 + -88k + -4k2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + -88k + -4k2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(27 + 22k + k2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(27 + 22k + k2)' equal to zero and attempt to solve: Simplifying 27 + 22k + k2 = 0 Solving 27 + 22k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 22k + -27 + k2 = 0 + -27 Reorder the terms: 27 + -27 + 22k + k2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 22k + k2 = 0 + -27 22k + k2 = 0 + -27 Combine like terms: 0 + -27 = -27 22k + k2 = -27 The k term is 22k. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22k + 121 + k2 = -27 + 121 Reorder the terms: 121 + 22k + k2 = -27 + 121 Combine like terms: -27 + 121 = 94 121 + 22k + k2 = 94 Factor a perfect square on the left side: (k + 11)(k + 11) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (k + 11) equal to 9.695359715 and -9.695359715.Subproblem 1
k + 11 = 9.695359715 Simplifying k + 11 = 9.695359715 Reorder the terms: 11 + k = 9.695359715 Solving 11 + k = 9.695359715 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + k = 9.695359715 + -11 Combine like terms: 11 + -11 = 0 0 + k = 9.695359715 + -11 k = 9.695359715 + -11 Combine like terms: 9.695359715 + -11 = -1.304640285 k = -1.304640285 Simplifying k = -1.304640285Subproblem 2
k + 11 = -9.695359715 Simplifying k + 11 = -9.695359715 Reorder the terms: 11 + k = -9.695359715 Solving 11 + k = -9.695359715 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + k = -9.695359715 + -11 Combine like terms: 11 + -11 = 0 0 + k = -9.695359715 + -11 k = -9.695359715 + -11 Combine like terms: -9.695359715 + -11 = -20.695359715 k = -20.695359715 Simplifying k = -20.695359715Solution
The solution to the problem is based on the solutions from the subproblems. k = {-1.304640285, -20.695359715}Solution
k = {-1.304640285, -20.695359715}
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