4x^4-2x^2-7=0

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Solution for 4x^4-2x^2-7=0 equation: 


Simplifying
4x4 + -2x2 + -7 = 0

Reorder the terms:
-7 + -2x2 + 4x4 = 0

Solving
-7 + -2x2 + 4x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-1.75 + -0.5x2 + x4 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -0.5x2 + 1.75 + x4 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -0.5x2 + x4 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -0.5x2 + x4 = 0 + 1.75
-0.5x2 + x4 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-0.5x2 + x4 = 1.75

The x term is -0.5x2.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x2 + 0.0625 + x4 = 1.75 + 0.0625

Reorder the terms:
0.0625 + -0.5x2 + x4 = 1.75 + 0.0625

Combine like terms: 1.75 + 0.0625 = 1.8125
0.0625 + -0.5x2 + x4 = 1.8125

Factor a perfect square on the left side:
(x2 + -0.25)(x2 + -0.25) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(x2 + -0.25) equal to 1.346291202 and -1.346291202.


Subproblem 1
x2 + -0.25 = 1.346291202

Simplifying
x2 + -0.25 = 1.346291202

Reorder the terms:
-0.25 + x2 = 1.346291202

Solving
-0.25 + x2 = 1.346291202

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x2 = 1.346291202 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x2 = 1.346291202 + 0.25
x2 = 1.346291202 + 0.25

Combine like terms: 1.346291202 + 0.25 = 1.596291202
x2 = 1.596291202

Simplifying
x2 = 1.596291202

Take the square root of each side:
x = {-1.263444182, 1.263444182}


Subproblem 2
x2 + -0.25 = -1.346291202

Simplifying
x2 + -0.25 = -1.346291202

Reorder the terms:
-0.25 + x2 = -1.346291202

Solving
-0.25 + x2 = -1.346291202

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x2 = -1.346291202 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x2 = -1.346291202 + 0.25
x2 = -1.346291202 + 0.25

Combine like terms: -1.346291202 + 0.25 = -1.096291202
x2 = -1.096291202

Simplifying
x2 = -1.096291202

Reorder the terms:
1.096291202 + x2 = -1.096291202 + 1.096291202

Combine like terms: -1.096291202 + 1.096291202 = 0.000000000
1.096291202 + 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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