x^2+22x+50=0

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Solution for x^2+22x+50=0 equation:


Simplifying
x2 + 22x + 50 = 0

Reorder the terms:
50 + 22x + x2 = 0

Solving
50 + 22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + 22x + -50 + x2 = 0 + -50

Reorder the terms:
50 + -50 + 22x + x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + 22x + x2 = 0 + -50
22x + x2 = 0 + -50

Combine like terms: 0 + -50 = -50
22x + x2 = -50

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -50 + 121

Reorder the terms:
121 + 22x + x2 = -50 + 121

Combine like terms: -50 + 121 = 71
121 + 22x + x2 = 71

Factor a perfect square on the left side:
(x + 11)(x + 11) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 11) equal to 8.426149773 and -8.426149773.

Subproblem 1

x + 11 = 8.426149773 Simplifying x + 11 = 8.426149773 Reorder the terms: 11 + x = 8.426149773 Solving 11 + x = 8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 8.426149773 + -11 Combine like terms: 11 + -11 = 0 0 + x = 8.426149773 + -11 x = 8.426149773 + -11 Combine like terms: 8.426149773 + -11 = -2.573850227 x = -2.573850227 Simplifying x = -2.573850227

Subproblem 2

x + 11 = -8.426149773 Simplifying x + 11 = -8.426149773 Reorder the terms: 11 + x = -8.426149773 Solving 11 + x = -8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -8.426149773 + -11 Combine like terms: 11 + -11 = 0 0 + x = -8.426149773 + -11 x = -8.426149773 + -11 Combine like terms: -8.426149773 + -11 = -19.426149773 x = -19.426149773 Simplifying x = -19.426149773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.573850227, -19.426149773}

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