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Simplifying 0 = -1x4 + 8x2 + -2 Reorder the terms: 0 = -2 + 8x2 + -1x4 Solving 0 = -2 + 8x2 + -1x4 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + -8x2 + x4 = -2 + 8x2 + -1x4 + 2 + -8x2 + x4 Reorder the terms: 2 + -8x2 + x4 = -2 + 2 + 8x2 + -8x2 + -1x4 + x4 Combine like terms: -2 + 2 = 0 2 + -8x2 + x4 = 0 + 8x2 + -8x2 + -1x4 + x4 2 + -8x2 + x4 = 8x2 + -8x2 + -1x4 + x4 Combine like terms: 8x2 + -8x2 = 0 2 + -8x2 + x4 = 0 + -1x4 + x4 2 + -8x2 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 2 + -8x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -8x2 + -2 + x4 = 0 + -2 Reorder the terms: 2 + -2 + -8x2 + x4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -8x2 + x4 = 0 + -2 -8x2 + x4 = 0 + -2 Combine like terms: 0 + -2 = -2 -8x2 + x4 = -2 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 = -2 + 16 Reorder the terms: 16 + -8x2 + x4 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + -8x2 + x4 = 14 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x2 + -4) equal to 3.741657387 and -3.741657387.Subproblem 1
x2 + -4 = 3.741657387 Simplifying x2 + -4 = 3.741657387 Reorder the terms: -4 + x2 = 3.741657387 Solving -4 + x2 = 3.741657387 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 = 3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.741657387 + 4 x2 = 3.741657387 + 4 Combine like terms: 3.741657387 + 4 = 7.741657387 x2 = 7.741657387 Simplifying x2 = 7.741657387 Take the square root of each side: x = {-2.7823834, 2.7823834}Subproblem 2
x2 + -4 = -3.741657387 Simplifying x2 + -4 = -3.741657387 Reorder the terms: -4 + x2 = -3.741657387 Solving -4 + x2 = -3.741657387 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 = -3.741657387 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.741657387 + 4 x2 = -3.741657387 + 4 Combine like terms: -3.741657387 + 4 = 0.258342613 x2 = 0.258342613 Simplifying x2 = 0.258342613 Take the square root of each side: x = {-0.508274151, 0.508274151}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.7823834, 2.7823834, -0.508274151, 0.508274151}
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