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Simplifying x4 + -16x2 + 35 = 0 Reorder the terms: 35 + -16x2 + x4 = 0 Solving 35 + -16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -16x2 + -35 + x4 = 0 + -35 Reorder the terms: 35 + -35 + -16x2 + x4 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -16x2 + x4 = 0 + -35 -16x2 + x4 = 0 + -35 Combine like terms: 0 + -35 = -35 -16x2 + x4 = -35 The x term is -16x2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x2 + 64 + x4 = -35 + 64 Reorder the terms: 64 + -16x2 + x4 = -35 + 64 Combine like terms: -35 + 64 = 29 64 + -16x2 + x4 = 29 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x2 + -8) equal to 5.385164807 and -5.385164807.Subproblem 1
x2 + -8 = 5.385164807 Simplifying x2 + -8 = 5.385164807 Reorder the terms: -8 + x2 = 5.385164807 Solving -8 + x2 = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 5.385164807 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 5.385164807 + 8 x2 = 5.385164807 + 8 Combine like terms: 5.385164807 + 8 = 13.385164807 x2 = 13.385164807 Simplifying x2 = 13.385164807 Take the square root of each side: x = {-3.658574149, 3.658574149}Subproblem 2
x2 + -8 = -5.385164807 Simplifying x2 + -8 = -5.385164807 Reorder the terms: -8 + x2 = -5.385164807 Solving -8 + x2 = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -5.385164807 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -5.385164807 + 8 x2 = -5.385164807 + 8 Combine like terms: -5.385164807 + 8 = 2.614835193 x2 = 2.614835193 Simplifying x2 = 2.614835193 Take the square root of each side: x = {-1.617045204, 1.617045204}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.658574149, 3.658574149, -1.617045204, 1.617045204}
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