x^2+33x+41=0

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Solution for x^2+33x+41=0 equation:


Simplifying
x2 + 33x + 41 = 0

Reorder the terms:
41 + 33x + x2 = 0

Solving
41 + 33x + 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 + 33x + -41 + x2 = 0 + -41

Reorder the terms:
41 + -41 + 33x + x2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 33x + x2 = 0 + -41
33x + x2 = 0 + -41

Combine like terms: 0 + -41 = -41
33x + x2 = -41

The x term is 33x.  Take half its coefficient (16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
33x + 272.25 + x2 = -41 + 272.25

Reorder the terms:
272.25 + 33x + x2 = -41 + 272.25

Combine like terms: -41 + 272.25 = 231.25
272.25 + 33x + x2 = 231.25

Factor a perfect square on the left side:
(x + 16.5)(x + 16.5) = 231.25

Calculate the square root of the right side: 15.206906326

Break this problem into two subproblems by setting 
(x + 16.5) equal to 15.206906326 and -15.206906326.

Subproblem 1

x + 16.5 = 15.206906326 Simplifying x + 16.5 = 15.206906326 Reorder the terms: 16.5 + x = 15.206906326 Solving 16.5 + x = 15.206906326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = 15.206906326 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 15.206906326 + -16.5 x = 15.206906326 + -16.5 Combine like terms: 15.206906326 + -16.5 = -1.293093674 x = -1.293093674 Simplifying x = -1.293093674

Subproblem 2

x + 16.5 = -15.206906326 Simplifying x + 16.5 = -15.206906326 Reorder the terms: 16.5 + x = -15.206906326 Solving 16.5 + x = -15.206906326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = -15.206906326 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -15.206906326 + -16.5 x = -15.206906326 + -16.5 Combine like terms: -15.206906326 + -16.5 = -31.706906326 x = -31.706906326 Simplifying x = -31.706906326

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.293093674, -31.706906326}

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