x^2+44x-215=0

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Solution for x^2+44x-215=0 equation: 


Simplifying
x2 + 44x + -215 = 0

Reorder the terms:
-215 + 44x + x2 = 0

Solving
-215 + 44x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '215' to each side of the equation.
-215 + 44x + 215 + x2 = 0 + 215

Reorder the terms:
-215 + 215 + 44x + x2 = 0 + 215

Combine like terms: -215 + 215 = 0
0 + 44x + x2 = 0 + 215
44x + x2 = 0 + 215

Combine like terms: 0 + 215 = 215
44x + x2 = 215

The x term is 44x.  Take half its coefficient (22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
44x + 484 + x2 = 215 + 484

Reorder the terms:
484 + 44x + x2 = 215 + 484

Combine like terms: 215 + 484 = 699
484 + 44x + x2 = 699

Factor a perfect square on the left side:
(x + 22)(x + 22) = 699

Calculate the square root of the right side: 26.438608133

Break this problem into two subproblems by setting 
(x + 22) equal to 26.438608133 and -26.438608133.


Subproblem 1
x + 22 = 26.438608133

Simplifying
x + 22 = 26.438608133

Reorder the terms:
22 + x = 26.438608133

Solving
22 + x = 26.438608133

Solving for variable 'x'.

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

Add '-22' to each side of the equation.
22 + -22 + x = 26.438608133 + -22

Combine like terms: 22 + -22 = 0
0 + x = 26.438608133 + -22
x = 26.438608133 + -22

Combine like terms: 26.438608133 + -22 = 4.438608133
x = 4.438608133

Simplifying
x = 4.438608133


Subproblem 2
x + 22 = -26.438608133

Simplifying
x + 22 = -26.438608133

Reorder the terms:
22 + x = -26.438608133

Solving
22 + x = -26.438608133

Solving for variable 'x'.

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

Add '-22' to each side of the equation.
22 + -22 + x = -26.438608133 + -22

Combine like terms: 22 + -22 = 0
0 + x = -26.438608133 + -22
x = -26.438608133 + -22

Combine like terms: -26.438608133 + -22 = -48.438608133
x = -48.438608133

Simplifying
x = -48.438608133


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.438608133, -48.438608133}

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