4q^4-4q^2-1=0

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Solution for 4q^4-4q^2-1=0 equation:


Simplifying
4q4 + -4q2 + -1 = 0

Reorder the terms:
-1 + -4q2 + 4q4 = 0

Solving
-1 + -4q2 + 4q4 = 0

Solving for variable 'q'.

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

Divide each side by '4'.
-0.25 + -1q2 + q4 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1q2 + 0.25 + q4 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1q2 + q4 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1q2 + q4 = 0 + 0.25
-1q2 + q4 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1q2 + q4 = 0.25

The q term is -1q2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1q2 + 0.25 + q4 = 0.25 + 0.25

Reorder the terms:
0.25 + -1q2 + q4 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + -1q2 + q4 = 0.5

Factor a perfect square on the left side:
(q2 + -0.5)(q2 + -0.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(q2 + -0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1

q2 + -0.5 = 0.707106781 Simplifying q2 + -0.5 = 0.707106781 Reorder the terms: -0.5 + q2 = 0.707106781 Solving -0.5 + q2 = 0.707106781 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + q2 = 0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + q2 = 0.707106781 + 0.5 q2 = 0.707106781 + 0.5 Combine like terms: 0.707106781 + 0.5 = 1.207106781 q2 = 1.207106781 Simplifying q2 = 1.207106781 Take the square root of each side: q = {-1.098684113, 1.098684113}

Subproblem 2

q2 + -0.5 = -0.707106781 Simplifying q2 + -0.5 = -0.707106781 Reorder the terms: -0.5 + q2 = -0.707106781 Solving -0.5 + q2 = -0.707106781 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + q2 = -0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + q2 = -0.707106781 + 0.5 q2 = -0.707106781 + 0.5 Combine like terms: -0.707106781 + 0.5 = -0.207106781 q2 = -0.207106781 Simplifying q2 = -0.207106781 Reorder the terms: 0.207106781 + q2 = -0.207106781 + 0.207106781 Combine like terms: -0.207106781 + 0.207106781 = 0.000000000 0.207106781 + q2 = 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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