x^2+4x-41=0

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Solution for x^2+4x-41=0 equation: 


Simplifying
x2 + 4x + -41 = 0

Reorder the terms:
-41 + 4x + x2 = 0

Solving
-41 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 4x + 41 + x2 = 0 + 41

Reorder the terms:
-41 + 41 + 4x + x2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 4x + x2 = 0 + 41
4x + x2 = 0 + 41

Combine like terms: 0 + 41 = 41
4x + x2 = 41

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 41 + 4

Reorder the terms:
4 + 4x + x2 = 41 + 4

Combine like terms: 41 + 4 = 45
4 + 4x + x2 = 45

Factor a perfect square on the left side:
(x + 2)(x + 2) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 2) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + 2 = 6.708203933

Simplifying
x + 2 = 6.708203933

Reorder the terms:
2 + x = 6.708203933

Solving
2 + x = 6.708203933

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 6.708203933 + -2

Combine like terms: 2 + -2 = 0
0 + x = 6.708203933 + -2
x = 6.708203933 + -2

Combine like terms: 6.708203933 + -2 = 4.708203933
x = 4.708203933

Simplifying
x = 4.708203933


Subproblem 2
x + 2 = -6.708203933

Simplifying
x + 2 = -6.708203933

Reorder the terms:
2 + x = -6.708203933

Solving
2 + x = -6.708203933

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -6.708203933 + -2

Combine like terms: 2 + -2 = 0
0 + x = -6.708203933 + -2
x = -6.708203933 + -2

Combine like terms: -6.708203933 + -2 = -8.708203933
x = -8.708203933

Simplifying
x = -8.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.708203933, -8.708203933}

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