x^4-3.75x^2-1=0

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Solution for x^4-3.75x^2-1=0 equation: 


Simplifying
x4 + -3.75x2 + -1 = 0

Reorder the terms:
-1 + -3.75x2 + x4 = 0

Solving
-1 + -3.75x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3.75x2 + 1 + x4 = 0 + 1

Reorder the terms:
-1 + 1 + -3.75x2 + x4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3.75x2 + x4 = 0 + 1
-3.75x2 + x4 = 0 + 1

Combine like terms: 0 + 1 = 1
-3.75x2 + x4 = 1

The x term is -3.75x2.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x2 + 3.515625 + x4 = 1 + 3.515625

Reorder the terms:
3.515625 + -3.75x2 + x4 = 1 + 3.515625

Combine like terms: 1 + 3.515625 = 4.515625
3.515625 + -3.75x2 + x4 = 4.515625

Factor a perfect square on the left side:
(x2 + -1.875)(x2 + -1.875) = 4.515625

Calculate the square root of the right side: 2.125

Break this problem into two subproblems by setting 
(x2 + -1.875) equal to 2.125 and -2.125.


Subproblem 1
x2 + -1.875 = 2.125

Simplifying
x2 + -1.875 = 2.125

Reorder the terms:
-1.875 + x2 = 2.125

Solving
-1.875 + x2 = 2.125

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x2 = 2.125 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x2 = 2.125 + 1.875
x2 = 2.125 + 1.875

Combine like terms: 2.125 + 1.875 = 4
x2 = 4

Simplifying
x2 = 4

Take the square root of each side:
x = {-2, 2}


Subproblem 2
x2 + -1.875 = -2.125

Simplifying
x2 + -1.875 = -2.125

Reorder the terms:
-1.875 + x2 = -2.125

Solving
-1.875 + x2 = -2.125

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x2 = -2.125 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x2 = -2.125 + 1.875
x2 = -2.125 + 1.875

Combine like terms: -2.125 + 1.875 = -0.25
x2 = -0.25

Simplifying
x2 = -0.25

Reorder the terms:
0.25 + x2 = -0.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + x2 = 0.00

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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