874=41x+x^2

Solution for 874=41x+x^2 equation:

Simplifying
874 = 41x + x2

Solving
874 = 41x + x2

Solving for variable 'x'.

Reorder the terms:
874 + -41x + -1x2 = 41x + -41x + x2 + -1x2

Combine like terms: 41x + -41x = 0
874 + -41x + -1x2 = 0 + x2 + -1x2
874 + -41x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
874 + -41x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-874 + 41x + x2 = 0

Move the constant term to the right:

Add '874' to each side of the equation.
-874 + 41x + 874 + x2 = 0 + 874

Reorder the terms:
-874 + 874 + 41x + x2 = 0 + 874

Combine like terms: -874 + 874 = 0
0 + 41x + x2 = 0 + 874
41x + x2 = 0 + 874

Combine like terms: 0 + 874 = 874
41x + x2 = 874

The x term is 41x.  Take half its coefficient (20.5).
Square it (420.25) and add it to both sides.

Add '420.25' to each side of the equation.
41x + 420.25 + x2 = 874 + 420.25

Reorder the terms:
420.25 + 41x + x2 = 874 + 420.25

Combine like terms: 874 + 420.25 = 1294.25
420.25 + 41x + x2 = 1294.25

Factor a perfect square on the left side:
(x + 20.5)(x + 20.5) = 1294.25

Calculate the square root of the right side: 35.975686234

Break this problem into two subproblems by setting 
(x + 20.5) equal to 35.975686234 and -35.975686234.

Subproblem 1
x + 20.5 = 35.975686234

Simplifying
x + 20.5 = 35.975686234

Reorder the terms:
20.5 + x = 35.975686234

Solving
20.5 + x = 35.975686234

Solving for variable 'x'.

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

Add '-20.5' to each side of the equation.
20.5 + -20.5 + x = 35.975686234 + -20.5

Combine like terms: 20.5 + -20.5 = 0.0
0.0 + x = 35.975686234 + -20.5
x = 35.975686234 + -20.5

Combine like terms: 35.975686234 + -20.5 = 15.475686234
x = 15.475686234

Simplifying
x = 15.475686234

Subproblem 2
x + 20.5 = -35.975686234

Simplifying
x + 20.5 = -35.975686234

Reorder the terms:
20.5 + x = -35.975686234

Solving
20.5 + x = -35.975686234

Solving for variable 'x'.

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

Add '-20.5' to each side of the equation.
20.5 + -20.5 + x = -35.975686234 + -20.5

Combine like terms: 20.5 + -20.5 = 0.0
0.0 + x = -35.975686234 + -20.5
x = -35.975686234 + -20.5

Combine like terms: -35.975686234 + -20.5 = -56.475686234
x = -56.475686234

Simplifying
x = -56.475686234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.475686234, -56.475686234}