[4(q*q)]-1=0

Solution for [4(q*q)]-1=0 equation:

Simplifying
[4(q * q)] + -1 = 0

Multiply q * q
[4(q2)] + -1 = 0

Reorder the terms:
-1 + [4q2] = 0

Solving
-1 + [4q2] = 0

Solving for variable 'q'.

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

Add '1' to each side of the equation.
-1 + 1 + [4q2] = 0 + 1

Combine like terms: -1 + 1 = 0
0 + [4q2] = 0 + 1
[4q2] = 0 + 1

Combine like terms: 0 + 1 = 1
[4q2] = 1

Divide each side by '4'.
q2 = 0.25

Simplifying
q2 = 0.25

Take the square root of each side:
q = {-0.5, 0.5}