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Simplifying (-4k4 + 14 + 3k2) + (3k4 + -14k2 + -8) = 0 Reorder the terms: (14 + 3k2 + -4k4) + (3k4 + -14k2 + -8) = 0 Remove parenthesis around (14 + 3k2 + -4k4) 14 + 3k2 + -4k4 + (3k4 + -14k2 + -8) = 0 Reorder the terms: 14 + 3k2 + -4k4 + (-8 + -14k2 + 3k4) = 0 Remove parenthesis around (-8 + -14k2 + 3k4) 14 + 3k2 + -4k4 + -8 + -14k2 + 3k4 = 0 Reorder the terms: 14 + -8 + 3k2 + -14k2 + -4k4 + 3k4 = 0 Combine like terms: 14 + -8 = 6 6 + 3k2 + -14k2 + -4k4 + 3k4 = 0 Combine like terms: 3k2 + -14k2 = -11k2 6 + -11k2 + -4k4 + 3k4 = 0 Combine like terms: -4k4 + 3k4 = -1k4 6 + -11k2 + -1k4 = 0 Solving 6 + -11k2 + -1k4 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + 11k2 + k4 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 11k2 + 6 + k4 = 0 + 6 Reorder the terms: -6 + 6 + 11k2 + k4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 11k2 + k4 = 0 + 6 11k2 + k4 = 0 + 6 Combine like terms: 0 + 6 = 6 11k2 + k4 = 6 The k term is 11k2. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11k2 + 30.25 + k4 = 6 + 30.25 Reorder the terms: 30.25 + 11k2 + k4 = 6 + 30.25 Combine like terms: 6 + 30.25 = 36.25 30.25 + 11k2 + k4 = 36.25 Factor a perfect square on the left side: (k2 + 5.5)(k2 + 5.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (k2 + 5.5) equal to 6.020797289 and -6.020797289.Subproblem 1
k2 + 5.5 = 6.020797289 Simplifying k2 + 5.5 = 6.020797289 Reorder the terms: 5.5 + k2 = 6.020797289 Solving 5.5 + k2 = 6.020797289 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + k2 = 6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + k2 = 6.020797289 + -5.5 k2 = 6.020797289 + -5.5 Combine like terms: 6.020797289 + -5.5 = 0.520797289 k2 = 0.520797289 Simplifying k2 = 0.520797289 Take the square root of each side: k = {-0.721662864, 0.721662864}Subproblem 2
k2 + 5.5 = -6.020797289 Simplifying k2 + 5.5 = -6.020797289 Reorder the terms: 5.5 + k2 = -6.020797289 Solving 5.5 + k2 = -6.020797289 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + k2 = -6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + k2 = -6.020797289 + -5.5 k2 = -6.020797289 + -5.5 Combine like terms: -6.020797289 + -5.5 = -11.520797289 k2 = -11.520797289 Simplifying k2 = -11.520797289 Reorder the terms: 11.520797289 + k2 = -11.520797289 + 11.520797289 Combine like terms: -11.520797289 + 11.520797289 = 0.000000000 11.520797289 + 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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