2x^2+5x=41

Solution for 2x^2+5x=41 equation:

Simplifying
2x2 + 5x = 41

Reorder the terms:
5x + 2x2 = 41

Solving
5x + 2x2 = 41

Solving for variable 'x'.

Reorder the terms:
-41 + 5x + 2x2 = 41 + -41

Combine like terms: 41 + -41 = 0
-41 + 5x + 2x2 = 0

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

Divide each side by '2'.
-20.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '20.5' to each side of the equation.
-20.5 + 2.5x + 20.5 + x2 = 0 + 20.5

Reorder the terms:
-20.5 + 20.5 + 2.5x + x2 = 0 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + 2.5x + x2 = 0 + 20.5
2.5x + x2 = 0 + 20.5

Combine like terms: 0 + 20.5 = 20.5
2.5x + x2 = 20.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 20.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 20.5 + 1.5625

Combine like terms: 20.5 + 1.5625 = 22.0625
1.5625 + 2.5x + x2 = 22.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 22.0625

Calculate the square root of the right side: 4.697073557

Break this problem into two subproblems by setting 
(x + 1.25) equal to 4.697073557 and -4.697073557.

Subproblem 1
x + 1.25 = 4.697073557

Simplifying
x + 1.25 = 4.697073557

Reorder the terms:
1.25 + x = 4.697073557

Solving
1.25 + x = 4.697073557

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 4.697073557 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 4.697073557 + -1.25
x = 4.697073557 + -1.25

Combine like terms: 4.697073557 + -1.25 = 3.447073557
x = 3.447073557

Simplifying
x = 3.447073557

Subproblem 2
x + 1.25 = -4.697073557

Simplifying
x + 1.25 = -4.697073557

Reorder the terms:
1.25 + x = -4.697073557

Solving
1.25 + x = -4.697073557

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -4.697073557 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -4.697073557 + -1.25
x = -4.697073557 + -1.25

Combine like terms: -4.697073557 + -1.25 = -5.947073557
x = -5.947073557

Simplifying
x = -5.947073557

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.447073557, -5.947073557}