1-4x^2-x-3=0

Solution for 1-4x^2-x-3=0 equation:

Simplifying
1 + -4x2 + -1x + -3 = 0

Reorder the terms:
1 + -3 + -1x + -4x2 = 0

Combine like terms: 1 + -3 = -2
-2 + -1x + -4x2 = 0

Solving
-2 + -1x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + x + 4x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + x + 4x2)' equal to zero and attempt to solve:

Simplifying
2 + x + 4x2 = 0

Solving
2 + x + 4x2 = 0

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

Divide each side by '4'.
0.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.25x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.25x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.25x + x2 = 0 + -0.5
0.25x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.25x + x2 = -0.5

The x term is x.  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.
0.25x + 0.25 + x2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.25x + x2 = -0.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.25

Can't calculate square root of the right side.

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.