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Simplifying 9x4 + -34x2 + 2 = 0 Reorder the terms: 2 + -34x2 + 9x4 = 0 Solving 2 + -34x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + -3.777777778x2 + x4 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -3.777777778x2 + -0.2222222222 + x4 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -3.777777778x2 + x4 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -3.777777778x2 + x4 = 0 + -0.2222222222 -3.777777778x2 + x4 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -3.777777778x2 + x4 = -0.2222222222 The x term is -3.777777778x2. Take half its coefficient (-1.888888889). Square it (3.567901235) and add it to both sides. Add '3.567901235' to each side of the equation. -3.777777778x2 + 3.567901235 + x4 = -0.2222222222 + 3.567901235 Reorder the terms: 3.567901235 + -3.777777778x2 + x4 = -0.2222222222 + 3.567901235 Combine like terms: -0.2222222222 + 3.567901235 = 3.3456790128 3.567901235 + -3.777777778x2 + x4 = 3.3456790128 Factor a perfect square on the left side: (x2 + -1.888888889)(x2 + -1.888888889) = 3.3456790128 Calculate the square root of the right side: 1.829119737 Break this problem into two subproblems by setting (x2 + -1.888888889) equal to 1.829119737 and -1.829119737.Subproblem 1
x2 + -1.888888889 = 1.829119737 Simplifying x2 + -1.888888889 = 1.829119737 Reorder the terms: -1.888888889 + x2 = 1.829119737 Solving -1.888888889 + x2 = 1.829119737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x2 = 1.829119737 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x2 = 1.829119737 + 1.888888889 x2 = 1.829119737 + 1.888888889 Combine like terms: 1.829119737 + 1.888888889 = 3.718008626 x2 = 3.718008626 Simplifying x2 = 3.718008626 Take the square root of each side: x = {-1.928213843, 1.928213843}Subproblem 2
x2 + -1.888888889 = -1.829119737 Simplifying x2 + -1.888888889 = -1.829119737 Reorder the terms: -1.888888889 + x2 = -1.829119737 Solving -1.888888889 + x2 = -1.829119737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x2 = -1.829119737 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x2 = -1.829119737 + 1.888888889 x2 = -1.829119737 + 1.888888889 Combine like terms: -1.829119737 + 1.888888889 = 0.059769152 x2 = 0.059769152 Simplifying x2 = 0.059769152 Take the square root of each side: x = {-0.244477304, 0.244477304}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.928213843, 1.928213843, -0.244477304, 0.244477304}
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