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Simplifying x4 + 8x2 + -36 = 0 Reorder the terms: -36 + 8x2 + x4 = 0 Solving -36 + 8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 8x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + 8x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 8x2 + x4 = 0 + 36 8x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 8x2 + x4 = 36 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 = 36 + 16 Reorder the terms: 16 + 8x2 + x4 = 36 + 16 Combine like terms: 36 + 16 = 52 16 + 8x2 + x4 = 52 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x2 + 4) equal to 7.211102551 and -7.211102551.Subproblem 1
x2 + 4 = 7.211102551 Simplifying x2 + 4 = 7.211102551 Reorder the terms: 4 + x2 = 7.211102551 Solving 4 + x2 = 7.211102551 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 = 7.211102551 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 7.211102551 + -4 x2 = 7.211102551 + -4 Combine like terms: 7.211102551 + -4 = 3.211102551 x2 = 3.211102551 Simplifying x2 = 3.211102551 Take the square root of each side: x = {-1.791954952, 1.791954952}Subproblem 2
x2 + 4 = -7.211102551 Simplifying x2 + 4 = -7.211102551 Reorder the terms: 4 + x2 = -7.211102551 Solving 4 + x2 = -7.211102551 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 = -7.211102551 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -7.211102551 + -4 x2 = -7.211102551 + -4 Combine like terms: -7.211102551 + -4 = -11.211102551 x2 = -11.211102551 Simplifying x2 = -11.211102551 Reorder the terms: 11.211102551 + x2 = -11.211102551 + 11.211102551 Combine like terms: -11.211102551 + 11.211102551 = 0.000000000 11.211102551 + 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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