16x^2-377x+1073=0

Solution for 16x^2-377x+1073=0 equation:

Simplifying
16x2 + -377x + 1073 = 0

Reorder the terms:
1073 + -377x + 16x2 = 0

Solving
1073 + -377x + 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'.
67.0625 + -23.5625x + x2 = 0

Move the constant term to the right:

Add '-67.0625' to each side of the equation.
67.0625 + -23.5625x + -67.0625 + x2 = 0 + -67.0625

Reorder the terms:
67.0625 + -67.0625 + -23.5625x + x2 = 0 + -67.0625

Combine like terms: 67.0625 + -67.0625 = 0.0000
0.0000 + -23.5625x + x2 = 0 + -67.0625
-23.5625x + x2 = 0 + -67.0625

Combine like terms: 0 + -67.0625 = -67.0625
-23.5625x + x2 = -67.0625

The x term is -23.5625x.  Take half its coefficient (-11.78125).
Square it (138.7978516) and add it to both sides.

Add '138.7978516' to each side of the equation.
-23.5625x + 138.7978516 + x2 = -67.0625 + 138.7978516

Reorder the terms:
138.7978516 + -23.5625x + x2 = -67.0625 + 138.7978516

Combine like terms: -67.0625 + 138.7978516 = 71.7353516
138.7978516 + -23.5625x + x2 = 71.7353516

Factor a perfect square on the left side:
(x + -11.78125)(x + -11.78125) = 71.7353516

Calculate the square root of the right side: 8.469672461

Break this problem into two subproblems by setting 
(x + -11.78125) equal to 8.469672461 and -8.469672461.

Subproblem 1
x + -11.78125 = 8.469672461

Simplifying
x + -11.78125 = 8.469672461

Reorder the terms:
-11.78125 + x = 8.469672461

Solving
-11.78125 + x = 8.469672461

Solving for variable 'x'.

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

Add '11.78125' to each side of the equation.
-11.78125 + 11.78125 + x = 8.469672461 + 11.78125

Combine like terms: -11.78125 + 11.78125 = 0.00000
0.00000 + x = 8.469672461 + 11.78125
x = 8.469672461 + 11.78125

Combine like terms: 8.469672461 + 11.78125 = 20.250922461
x = 20.250922461

Simplifying
x = 20.250922461

Subproblem 2
x + -11.78125 = -8.469672461

Simplifying
x + -11.78125 = -8.469672461

Reorder the terms:
-11.78125 + x = -8.469672461

Solving
-11.78125 + x = -8.469672461

Solving for variable 'x'.

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

Add '11.78125' to each side of the equation.
-11.78125 + 11.78125 + x = -8.469672461 + 11.78125

Combine like terms: -11.78125 + 11.78125 = 0.00000
0.00000 + x = -8.469672461 + 11.78125
x = -8.469672461 + 11.78125

Combine like terms: -8.469672461 + 11.78125 = 3.311577539
x = 3.311577539

Simplifying
x = 3.311577539

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.250922461, 3.311577539}