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Simplifying x4 + 8x2 + -8 = 0 Reorder the terms: -8 + 8x2 + x4 = 0 Solving -8 + 8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 8x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + 8x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 8x2 + x4 = 0 + 8 8x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 8x2 + x4 = 8 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 = 8 + 16 Reorder the terms: 16 + 8x2 + x4 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + 8x2 + x4 = 24 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x2 + 4) equal to 4.898979486 and -4.898979486.Subproblem 1
x2 + 4 = 4.898979486 Simplifying x2 + 4 = 4.898979486 Reorder the terms: 4 + x2 = 4.898979486 Solving 4 + x2 = 4.898979486 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 = 4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 4.898979486 + -4 x2 = 4.898979486 + -4 Combine like terms: 4.898979486 + -4 = 0.898979486 x2 = 0.898979486 Simplifying x2 = 0.898979486 Take the square root of each side: x = {-0.948145287, 0.948145287}Subproblem 2
x2 + 4 = -4.898979486 Simplifying x2 + 4 = -4.898979486 Reorder the terms: 4 + x2 = -4.898979486 Solving 4 + x2 = -4.898979486 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 = -4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -4.898979486 + -4 x2 = -4.898979486 + -4 Combine like terms: -4.898979486 + -4 = -8.898979486 x2 = -8.898979486 Simplifying x2 = -8.898979486 Reorder the terms: 8.898979486 + x2 = -8.898979486 + 8.898979486 Combine like terms: -8.898979486 + 8.898979486 = 0.000000000 8.898979486 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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