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Simplifying x4 + -162x2 + 50 = 0 Reorder the terms: 50 + -162x2 + x4 = 0 Solving 50 + -162x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -162x2 + -50 + x4 = 0 + -50 Reorder the terms: 50 + -50 + -162x2 + x4 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -162x2 + x4 = 0 + -50 -162x2 + x4 = 0 + -50 Combine like terms: 0 + -50 = -50 -162x2 + x4 = -50 The x term is -162x2. Take half its coefficient (-81). Square it (6561) and add it to both sides. Add '6561' to each side of the equation. -162x2 + 6561 + x4 = -50 + 6561 Reorder the terms: 6561 + -162x2 + x4 = -50 + 6561 Combine like terms: -50 + 6561 = 6511 6561 + -162x2 + x4 = 6511 Factor a perfect square on the left side: (x2 + -81)(x2 + -81) = 6511 Calculate the square root of the right side: 80.690767749 Break this problem into two subproblems by setting (x2 + -81) equal to 80.690767749 and -80.690767749.Subproblem 1
x2 + -81 = 80.690767749 Simplifying x2 + -81 = 80.690767749 Reorder the terms: -81 + x2 = 80.690767749 Solving -81 + x2 = 80.690767749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81' to each side of the equation. -81 + 81 + x2 = 80.690767749 + 81 Combine like terms: -81 + 81 = 0 0 + x2 = 80.690767749 + 81 x2 = 80.690767749 + 81 Combine like terms: 80.690767749 + 81 = 161.690767749 x2 = 161.690767749 Simplifying x2 = 161.690767749 Take the square root of each side: x = {-12.715768469, 12.715768469}Subproblem 2
x2 + -81 = -80.690767749 Simplifying x2 + -81 = -80.690767749 Reorder the terms: -81 + x2 = -80.690767749 Solving -81 + x2 = -80.690767749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '81' to each side of the equation. -81 + 81 + x2 = -80.690767749 + 81 Combine like terms: -81 + 81 = 0 0 + x2 = -80.690767749 + 81 x2 = -80.690767749 + 81 Combine like terms: -80.690767749 + 81 = 0.309232251 x2 = 0.309232251 Simplifying x2 = 0.309232251 Take the square root of each side: x = {-0.55608655, 0.55608655}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-12.715768469, 12.715768469, -0.55608655, 0.55608655}
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