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Simplifying 2k4 + 12k2 + 9 = 0 Reorder the terms: 9 + 12k2 + 2k4 = 0 Solving 9 + 12k2 + 2k4 = 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'. 4.5 + 6k2 + k4 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 6k2 + -4.5 + k4 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 6k2 + k4 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 6k2 + k4 = 0 + -4.5 6k2 + k4 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 6k2 + k4 = -4.5 The k term is 6k2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6k2 + 9 + k4 = -4.5 + 9 Reorder the terms: 9 + 6k2 + k4 = -4.5 + 9 Combine like terms: -4.5 + 9 = 4.5 9 + 6k2 + k4 = 4.5 Factor a perfect square on the left side: (k2 + 3)(k2 + 3) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (k2 + 3) equal to 2.121320344 and -2.121320344.Subproblem 1
k2 + 3 = 2.121320344 Simplifying k2 + 3 = 2.121320344 Reorder the terms: 3 + k2 = 2.121320344 Solving 3 + k2 = 2.121320344 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k2 = 2.121320344 + -3 Combine like terms: 3 + -3 = 0 0 + k2 = 2.121320344 + -3 k2 = 2.121320344 + -3 Combine like terms: 2.121320344 + -3 = -0.878679656 k2 = -0.878679656 Simplifying k2 = -0.878679656 Reorder the terms: 0.878679656 + k2 = -0.878679656 + 0.878679656 Combine like terms: -0.878679656 + 0.878679656 = 0.000000000 0.878679656 + k2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
k2 + 3 = -2.121320344 Simplifying k2 + 3 = -2.121320344 Reorder the terms: 3 + k2 = -2.121320344 Solving 3 + k2 = -2.121320344 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + k2 = -2.121320344 + -3 Combine like terms: 3 + -3 = 0 0 + k2 = -2.121320344 + -3 k2 = -2.121320344 + -3 Combine like terms: -2.121320344 + -3 = -5.121320344 k2 = -5.121320344 Simplifying k2 = -5.121320344 Reorder the terms: 5.121320344 + k2 = -5.121320344 + 5.121320344 Combine like terms: -5.121320344 + 5.121320344 = 0.000000000 5.121320344 + k2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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