x^4-8x^2+4=0

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Solution for x^4-8x^2+4=0 equation:


Simplifying
x4 + -8x2 + 4 = 0

Reorder the terms:
4 + -8x2 + x4 = 0

Solving
4 + -8x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -8x2 + -4 + x4 = 0 + -4

Reorder the terms:
4 + -4 + -8x2 + x4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -8x2 + x4 = 0 + -4
-8x2 + x4 = 0 + -4

Combine like terms: 0 + -4 = -4
-8x2 + x4 = -4

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 = -4 + 16

Reorder the terms:
16 + -8x2 + x4 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + -8x2 + x4 = 12

Factor a perfect square on the left side:
(x2 + -4)(x2 + -4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x2 + -4) equal to 3.464101615 and -3.464101615.

Subproblem 1

x2 + -4 = 3.464101615 Simplifying x2 + -4 = 3.464101615 Reorder the terms: -4 + x2 = 3.464101615 Solving -4 + x2 = 3.464101615 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 = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.464101615 + 4 x2 = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 x2 = 7.464101615 Simplifying x2 = 7.464101615 Take the square root of each side: x = {-2.732050808, 2.732050808}

Subproblem 2

x2 + -4 = -3.464101615 Simplifying x2 + -4 = -3.464101615 Reorder the terms: -4 + x2 = -3.464101615 Solving -4 + x2 = -3.464101615 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 = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.464101615 + 4 x2 = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 x2 = 0.535898385 Simplifying x2 = 0.535898385 Take the square root of each side: x = {-0.732050808, 0.732050808}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.732050808, 2.732050808, -0.732050808, 0.732050808}

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