x^4-16x^2+26=0

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Solution for x^4-16x^2+26=0 equation:


Simplifying
x4 + -16x2 + 26 = 0

Reorder the terms:
26 + -16x2 + x4 = 0

Solving
26 + -16x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-26' to each side of the equation.
26 + -16x2 + -26 + x4 = 0 + -26

Reorder the terms:
26 + -26 + -16x2 + x4 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -16x2 + x4 = 0 + -26
-16x2 + x4 = 0 + -26

Combine like terms: 0 + -26 = -26
-16x2 + x4 = -26

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 = -26 + 64

Reorder the terms:
64 + -16x2 + x4 = -26 + 64

Combine like terms: -26 + 64 = 38
64 + -16x2 + x4 = 38

Factor a perfect square on the left side:
(x2 + -8)(x2 + -8) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x2 + -8) equal to 6.164414003 and -6.164414003.

Subproblem 1

x2 + -8 = 6.164414003 Simplifying x2 + -8 = 6.164414003 Reorder the terms: -8 + x2 = 6.164414003 Solving -8 + x2 = 6.164414003 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 = 6.164414003 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 6.164414003 + 8 x2 = 6.164414003 + 8 Combine like terms: 6.164414003 + 8 = 14.164414003 x2 = 14.164414003 Simplifying x2 = 14.164414003 Take the square root of each side: x = {-3.763564003, 3.763564003}

Subproblem 2

x2 + -8 = -6.164414003 Simplifying x2 + -8 = -6.164414003 Reorder the terms: -8 + x2 = -6.164414003 Solving -8 + x2 = -6.164414003 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 = -6.164414003 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -6.164414003 + 8 x2 = -6.164414003 + 8 Combine like terms: -6.164414003 + 8 = 1.835585997 x2 = 1.835585997 Simplifying x2 = 1.835585997 Take the square root of each side: x = {-1.354837997, 1.354837997}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.763564003, 3.763564003, -1.354837997, 1.354837997}

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