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Simplifying 2k2 + -8k + -26 = -12 Reorder the terms: -26 + -8k + 2k2 = -12 Solving -26 + -8k + 2k2 = -12 Solving for variable 'k'. Reorder the terms: -26 + 12 + -8k + 2k2 = -12 + 12 Combine like terms: -26 + 12 = -14 -14 + -8k + 2k2 = -12 + 12 Combine like terms: -12 + 12 = 0 -14 + -8k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -4k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -4k + k2)' equal to zero and attempt to solve: Simplifying -7 + -4k + k2 = 0 Solving -7 + -4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -4k + 7 + k2 = 0 + 7 Reorder the terms: -7 + 7 + -4k + k2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4k + k2 = 0 + 7 -4k + k2 = 0 + 7 Combine like terms: 0 + 7 = 7 -4k + k2 = 7 The k term is -4k. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4k + 4 + k2 = 7 + 4 Reorder the terms: 4 + -4k + k2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + -4k + k2 = 11 Factor a perfect square on the left side: (k + -2)(k + -2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (k + -2) equal to 3.31662479 and -3.31662479.Subproblem 1
k + -2 = 3.31662479 Simplifying k + -2 = 3.31662479 Reorder the terms: -2 + k = 3.31662479 Solving -2 + k = 3.31662479 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = 3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + k = 3.31662479 + 2 k = 3.31662479 + 2 Combine like terms: 3.31662479 + 2 = 5.31662479 k = 5.31662479 Simplifying k = 5.31662479Subproblem 2
k + -2 = -3.31662479 Simplifying k + -2 = -3.31662479 Reorder the terms: -2 + k = -3.31662479 Solving -2 + k = -3.31662479 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = -3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + k = -3.31662479 + 2 k = -3.31662479 + 2 Combine like terms: -3.31662479 + 2 = -1.31662479 k = -1.31662479 Simplifying k = -1.31662479Solution
The solution to the problem is based on the solutions from the subproblems. k = {5.31662479, -1.31662479}Solution
k = {5.31662479, -1.31662479}
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