4x^2-296x+85=

Solution for 4x^2-296x+85= equation:

Simplifying
4x2 + -296x + 85 = 0

Reorder the terms:
85 + -296x + 4x2 = 0

Solving
85 + -296x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
21.25 + -74x + x2 = 0

Move the constant term to the right:

Add '-21.25' to each side of the equation.
21.25 + -74x + -21.25 + x2 = 0 + -21.25

Reorder the terms:
21.25 + -21.25 + -74x + x2 = 0 + -21.25

Combine like terms: 21.25 + -21.25 = 0.00
0.00 + -74x + x2 = 0 + -21.25
-74x + x2 = 0 + -21.25

Combine like terms: 0 + -21.25 = -21.25
-74x + x2 = -21.25

The x term is -74x.  Take half its coefficient (-37).
Square it (1369) and add it to both sides.

Add '1369' to each side of the equation.
-74x + 1369 + x2 = -21.25 + 1369

Reorder the terms:
1369 + -74x + x2 = -21.25 + 1369

Combine like terms: -21.25 + 1369 = 1347.75
1369 + -74x + x2 = 1347.75

Factor a perfect square on the left side:
(x + -37)(x + -37) = 1347.75

Calculate the square root of the right side: 36.711714752

Break this problem into two subproblems by setting 
(x + -37) equal to 36.711714752 and -36.711714752.

Subproblem 1
x + -37 = 36.711714752

Simplifying
x + -37 = 36.711714752

Reorder the terms:
-37 + x = 36.711714752

Solving
-37 + x = 36.711714752

Solving for variable 'x'.

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

Add '37' to each side of the equation.
-37 + 37 + x = 36.711714752 + 37

Combine like terms: -37 + 37 = 0
0 + x = 36.711714752 + 37
x = 36.711714752 + 37

Combine like terms: 36.711714752 + 37 = 73.711714752
x = 73.711714752

Simplifying
x = 73.711714752

Subproblem 2
x + -37 = -36.711714752

Simplifying
x + -37 = -36.711714752

Reorder the terms:
-37 + x = -36.711714752

Solving
-37 + x = -36.711714752

Solving for variable 'x'.

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

Add '37' to each side of the equation.
-37 + 37 + x = -36.711714752 + 37

Combine like terms: -37 + 37 = 0
0 + x = -36.711714752 + 37
x = -36.711714752 + 37

Combine like terms: -36.711714752 + 37 = 0.288285248
x = 0.288285248

Simplifying
x = 0.288285248

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {73.711714752, 0.288285248}