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Simplifying 43.838x4 + 146.92x2 + -5534.42 = 0 Reorder the terms: -5534.42 + 146.92x2 + 43.838x4 = 0 Solving -5534.42 + 146.92x2 + 43.838x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 43.838 the coefficient of the squared term: Divide each side by '43.838'. -126.2470916 + 3.351430266x2 + x4 = 0 Move the constant term to the right: Add '126.2470916' to each side of the equation. -126.2470916 + 3.351430266x2 + 126.2470916 + x4 = 0 + 126.2470916 Reorder the terms: -126.2470916 + 126.2470916 + 3.351430266x2 + x4 = 0 + 126.2470916 Combine like terms: -126.2470916 + 126.2470916 = 0.0000000 0.0000000 + 3.351430266x2 + x4 = 0 + 126.2470916 3.351430266x2 + x4 = 0 + 126.2470916 Combine like terms: 0 + 126.2470916 = 126.2470916 3.351430266x2 + x4 = 126.2470916 The x term is 3.351430266x2. Take half its coefficient (1.675715133). Square it (2.808021207) and add it to both sides. Add '2.808021207' to each side of the equation. 3.351430266x2 + 2.808021207 + x4 = 126.2470916 + 2.808021207 Reorder the terms: 2.808021207 + 3.351430266x2 + x4 = 126.2470916 + 2.808021207 Combine like terms: 126.2470916 + 2.808021207 = 129.055112807 2.808021207 + 3.351430266x2 + x4 = 129.055112807 Factor a perfect square on the left side: (x2 + 1.675715133)(x2 + 1.675715133) = 129.055112807 Calculate the square root of the right side: 11.360242639 Break this problem into two subproblems by setting (x2 + 1.675715133) equal to 11.360242639 and -11.360242639.Subproblem 1
x2 + 1.675715133 = 11.360242639 Simplifying x2 + 1.675715133 = 11.360242639 Reorder the terms: 1.675715133 + x2 = 11.360242639 Solving 1.675715133 + x2 = 11.360242639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.675715133' to each side of the equation. 1.675715133 + -1.675715133 + x2 = 11.360242639 + -1.675715133 Combine like terms: 1.675715133 + -1.675715133 = 0.000000000 0.000000000 + x2 = 11.360242639 + -1.675715133 x2 = 11.360242639 + -1.675715133 Combine like terms: 11.360242639 + -1.675715133 = 9.684527506 x2 = 9.684527506 Simplifying x2 = 9.684527506 Take the square root of each side: x = {-3.11199735, 3.11199735}Subproblem 2
x2 + 1.675715133 = -11.360242639 Simplifying x2 + 1.675715133 = -11.360242639 Reorder the terms: 1.675715133 + x2 = -11.360242639 Solving 1.675715133 + x2 = -11.360242639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.675715133' to each side of the equation. 1.675715133 + -1.675715133 + x2 = -11.360242639 + -1.675715133 Combine like terms: 1.675715133 + -1.675715133 = 0.000000000 0.000000000 + x2 = -11.360242639 + -1.675715133 x2 = -11.360242639 + -1.675715133 Combine like terms: -11.360242639 + -1.675715133 = -13.035957772 x2 = -13.035957772 Simplifying x2 = -13.035957772 Reorder the terms: 13.035957772 + x2 = -13.035957772 + 13.035957772 Combine like terms: -13.035957772 + 13.035957772 = 0.000000000 13.035957772 + x2 = 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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