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Simplifying 0 = x4 + -8x2 + 1 Reorder the terms: 0 = 1 + -8x2 + x4 Solving 0 = 1 + -8x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 8x2 + -1x4 = 1 + -8x2 + x4 + -1 + 8x2 + -1x4 Reorder the terms: -1 + 8x2 + -1x4 = 1 + -1 + -8x2 + 8x2 + x4 + -1x4 Combine like terms: 1 + -1 = 0 -1 + 8x2 + -1x4 = 0 + -8x2 + 8x2 + x4 + -1x4 -1 + 8x2 + -1x4 = -8x2 + 8x2 + x4 + -1x4 Combine like terms: -8x2 + 8x2 = 0 -1 + 8x2 + -1x4 = 0 + x4 + -1x4 -1 + 8x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -1 + 8x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -8x2 + x4 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -8x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8x2 + x4 = 0 + -1 -8x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -8x2 + x4 = -1 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 = -1 + 16 Reorder the terms: 16 + -8x2 + x4 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + -8x2 + x4 = 15 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x2 + -4) equal to 3.872983346 and -3.872983346.Subproblem 1
x2 + -4 = 3.872983346 Simplifying x2 + -4 = 3.872983346 Reorder the terms: -4 + x2 = 3.872983346 Solving -4 + x2 = 3.872983346 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 = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.872983346 + 4 x2 = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 x2 = 7.872983346 Simplifying x2 = 7.872983346 Take the square root of each side: x = {-2.805883701, 2.805883701}Subproblem 2
x2 + -4 = -3.872983346 Simplifying x2 + -4 = -3.872983346 Reorder the terms: -4 + x2 = -3.872983346 Solving -4 + x2 = -3.872983346 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 = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.872983346 + 4 x2 = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 x2 = 0.127016654 Simplifying x2 = 0.127016654 Take the square root of each side: x = {-0.356393959, 0.356393959}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.805883701, 2.805883701, -0.356393959, 0.356393959}
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