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Simplifying 0.28019x4 + -5.599x2 + 1 = 0 Reorder the terms: 1 + -5.599x2 + 0.28019x4 = 0 Solving 1 + -5.599x2 + 0.28019x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.28019 the coefficient of the squared term: Divide each side by '0.28019'. 3.569006745 + -19.98286877x2 + x4 = 0 Move the constant term to the right: Add '-3.569006745' to each side of the equation. 3.569006745 + -19.98286877x2 + -3.569006745 + x4 = 0 + -3.569006745 Reorder the terms: 3.569006745 + -3.569006745 + -19.98286877x2 + x4 = 0 + -3.569006745 Combine like terms: 3.569006745 + -3.569006745 = 0.000000000 0.000000000 + -19.98286877x2 + x4 = 0 + -3.569006745 -19.98286877x2 + x4 = 0 + -3.569006745 Combine like terms: 0 + -3.569006745 = -3.569006745 -19.98286877x2 + x4 = -3.569006745 The x term is -19.98286877x2. Take half its coefficient (-9.991434385). Square it (99.82876107) and add it to both sides. Add '99.82876107' to each side of the equation. -19.98286877x2 + 99.82876107 + x4 = -3.569006745 + 99.82876107 Reorder the terms: 99.82876107 + -19.98286877x2 + x4 = -3.569006745 + 99.82876107 Combine like terms: -3.569006745 + 99.82876107 = 96.259754325 99.82876107 + -19.98286877x2 + x4 = 96.259754325 Factor a perfect square on the left side: (x2 + -9.991434385)(x2 + -9.991434385) = 96.259754325 Calculate the square root of the right side: 9.811205549 Break this problem into two subproblems by setting (x2 + -9.991434385) equal to 9.811205549 and -9.811205549.Subproblem 1
x2 + -9.991434385 = 9.811205549 Simplifying x2 + -9.991434385 = 9.811205549 Reorder the terms: -9.991434385 + x2 = 9.811205549 Solving -9.991434385 + x2 = 9.811205549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.991434385' to each side of the equation. -9.991434385 + 9.991434385 + x2 = 9.811205549 + 9.991434385 Combine like terms: -9.991434385 + 9.991434385 = 0.000000000 0.000000000 + x2 = 9.811205549 + 9.991434385 x2 = 9.811205549 + 9.991434385 Combine like terms: 9.811205549 + 9.991434385 = 19.802639934 x2 = 19.802639934 Simplifying x2 = 19.802639934 Take the square root of each side: x = {-4.450015723, 4.450015723}Subproblem 2
x2 + -9.991434385 = -9.811205549 Simplifying x2 + -9.991434385 = -9.811205549 Reorder the terms: -9.991434385 + x2 = -9.811205549 Solving -9.991434385 + x2 = -9.811205549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.991434385' to each side of the equation. -9.991434385 + 9.991434385 + x2 = -9.811205549 + 9.991434385 Combine like terms: -9.991434385 + 9.991434385 = 0.000000000 0.000000000 + x2 = -9.811205549 + 9.991434385 x2 = -9.811205549 + 9.991434385 Combine like terms: -9.811205549 + 9.991434385 = 0.180228836 x2 = 0.180228836 Simplifying x2 = 0.180228836 Take the square root of each side: x = {-0.424533669, 0.424533669}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.450015723, 4.450015723, -0.424533669, 0.424533669}
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