X^2+22X-380=0

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Solution for X^2+22X-380=0 equation: 


Simplifying
X2 + 22X + -380 = 0

Reorder the terms:
-380 + 22X + X2 = 0

Solving
-380 + 22X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '380' to each side of the equation.
-380 + 22X + 380 + X2 = 0 + 380

Reorder the terms:
-380 + 380 + 22X + X2 = 0 + 380

Combine like terms: -380 + 380 = 0
0 + 22X + X2 = 0 + 380
22X + X2 = 0 + 380

Combine like terms: 0 + 380 = 380
22X + X2 = 380

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 = 380 + 121

Reorder the terms:
121 + 22X + X2 = 380 + 121

Combine like terms: 380 + 121 = 501
121 + 22X + X2 = 501

Factor a perfect square on the left side:
(X + 11)(X + 11) = 501

Calculate the square root of the right side: 22.383029286

Break this problem into two subproblems by setting 
(X + 11) equal to 22.383029286 and -22.383029286.


Subproblem 1
X + 11 = 22.383029286

Simplifying
X + 11 = 22.383029286

Reorder the terms:
11 + X = 22.383029286

Solving
11 + X = 22.383029286

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 = 22.383029286 + -11

Combine like terms: 11 + -11 = 0
0 + X = 22.383029286 + -11
X = 22.383029286 + -11

Combine like terms: 22.383029286 + -11 = 11.383029286
X = 11.383029286

Simplifying
X = 11.383029286


Subproblem 2
X + 11 = -22.383029286

Simplifying
X + 11 = -22.383029286

Reorder the terms:
11 + X = -22.383029286

Solving
11 + X = -22.383029286

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 = -22.383029286 + -11

Combine like terms: 11 + -11 = 0
0 + X = -22.383029286 + -11
X = -22.383029286 + -11

Combine like terms: -22.383029286 + -11 = -33.383029286
X = -33.383029286

Simplifying
X = -33.383029286


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {11.383029286, -33.383029286}

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