16x^2+63x+4=0

Solution for 16x^2+63x+4=0 equation:

Simplifying
16x2 + 63x + 4 = 0

Reorder the terms:
4 + 63x + 16x2 = 0

Solving
4 + 63x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
0.25 + 3.9375x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 3.9375x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 3.9375x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 3.9375x + x2 = 0 + -0.25
3.9375x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
3.9375x + x2 = -0.25

The x term is 3.9375x.  Take half its coefficient (1.96875).
Square it (3.875976563) and add it to both sides.

Add '3.875976563' to each side of the equation.
3.9375x + 3.875976563 + x2 = -0.25 + 3.875976563

Reorder the terms:
3.875976563 + 3.9375x + x2 = -0.25 + 3.875976563

Combine like terms: -0.25 + 3.875976563 = 3.625976563
3.875976563 + 3.9375x + x2 = 3.625976563

Factor a perfect square on the left side:
(x + 1.96875)(x + 1.96875) = 3.625976563

Calculate the square root of the right side: 1.904199717

Break this problem into two subproblems by setting 
(x + 1.96875) equal to 1.904199717 and -1.904199717.

Subproblem 1
x + 1.96875 = 1.904199717

Simplifying
x + 1.96875 = 1.904199717

Reorder the terms:
1.96875 + x = 1.904199717

Solving
1.96875 + x = 1.904199717

Solving for variable 'x'.

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

Add '-1.96875' to each side of the equation.
1.96875 + -1.96875 + x = 1.904199717 + -1.96875

Combine like terms: 1.96875 + -1.96875 = 0.00000
0.00000 + x = 1.904199717 + -1.96875
x = 1.904199717 + -1.96875

Combine like terms: 1.904199717 + -1.96875 = -0.064550283
x = -0.064550283

Simplifying
x = -0.064550283

Subproblem 2
x + 1.96875 = -1.904199717

Simplifying
x + 1.96875 = -1.904199717

Reorder the terms:
1.96875 + x = -1.904199717

Solving
1.96875 + x = -1.904199717

Solving for variable 'x'.

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

Add '-1.96875' to each side of the equation.
1.96875 + -1.96875 + x = -1.904199717 + -1.96875

Combine like terms: 1.96875 + -1.96875 = 0.00000
0.00000 + x = -1.904199717 + -1.96875
x = -1.904199717 + -1.96875

Combine like terms: -1.904199717 + -1.96875 = -3.872949717
x = -3.872949717

Simplifying
x = -3.872949717

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.064550283, -3.872949717}