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Simplifying x4 + -8x2 + 14 = 0 Reorder the terms: 14 + -8x2 + x4 = 0 Solving 14 + -8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -8x2 + -14 + x4 = 0 + -14 Reorder the terms: 14 + -14 + -8x2 + x4 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -8x2 + x4 = 0 + -14 -8x2 + x4 = 0 + -14 Combine like terms: 0 + -14 = -14 -8x2 + x4 = -14 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -14 + 16 Reorder the terms: 16 + -8x2 + x4 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + -8x2 + x4 = 2 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x2 + -4) equal to 1.414213562 and -1.414213562.Subproblem 1
x2 + -4 = 1.414213562 Simplifying x2 + -4 = 1.414213562 Reorder the terms: -4 + x2 = 1.414213562 Solving -4 + x2 = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 1.414213562 + 4 x2 = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 x2 = 5.414213562 Simplifying x2 = 5.414213562 Take the square root of each side: x = {-2.32684627, 2.32684627}Subproblem 2
x2 + -4 = -1.414213562 Simplifying x2 + -4 = -1.414213562 Reorder the terms: -4 + x2 = -1.414213562 Solving -4 + x2 = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -1.414213562 + 4 x2 = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 x2 = 2.585786438 Simplifying x2 = 2.585786438 Take the square root of each side: x = {-1.608038071, 1.608038071}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.32684627, 2.32684627, -1.608038071, 1.608038071}
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