x^4-16x^2+4=0

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Solution for x^4-16x^2+4=0 equation:


Simplifying
x4 + -16x2 + 4 = 0

Reorder the terms:
4 + -16x2 + x4 = 0

Solving
4 + -16x2 + 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 + -16x2 + -4 + x4 = 0 + -4

Reorder the terms:
4 + -4 + -16x2 + x4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -16x2 + x4 = 0 + -4
-16x2 + x4 = 0 + -4

Combine like terms: 0 + -4 = -4
-16x2 + x4 = -4

The x term is -16x2.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x2 + 64 + x4 = -4 + 64

Reorder the terms:
64 + -16x2 + x4 = -4 + 64

Combine like terms: -4 + 64 = 60
64 + -16x2 + x4 = 60

Factor a perfect square on the left side:
(x2 + -8)(x2 + -8) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x2 + -8) equal to 7.745966692 and -7.745966692.

Subproblem 1

x2 + -8 = 7.745966692 Simplifying x2 + -8 = 7.745966692 Reorder the terms: -8 + x2 = 7.745966692 Solving -8 + x2 = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 7.745966692 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 7.745966692 + 8 x2 = 7.745966692 + 8 Combine like terms: 7.745966692 + 8 = 15.745966692 x2 = 15.745966692 Simplifying x2 = 15.745966692 Take the square root of each side: x = {-3.968118785, 3.968118785}

Subproblem 2

x2 + -8 = -7.745966692 Simplifying x2 + -8 = -7.745966692 Reorder the terms: -8 + x2 = -7.745966692 Solving -8 + x2 = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -7.745966692 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -7.745966692 + 8 x2 = -7.745966692 + 8 Combine like terms: -7.745966692 + 8 = 0.254033308 x2 = 0.254033308 Simplifying x2 = 0.254033308 Take the square root of each side: x = {-0.50401717, 0.50401717}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.968118785, 3.968118785, -0.50401717, 0.50401717}

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