X^2+10X+8=252

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Solution for X^2+10X+8=252 equation: 


Simplifying
X2 + 10X + 8 = 252

Reorder the terms:
8 + 10X + X2 = 252

Solving
8 + 10X + X2 = 252

Solving for variable 'X'.

Reorder the terms:
8 + -252 + 10X + X2 = 252 + -252

Combine like terms: 8 + -252 = -244
-244 + 10X + X2 = 252 + -252

Combine like terms: 252 + -252 = 0
-244 + 10X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '244' to each side of the equation.
-244 + 10X + 244 + X2 = 0 + 244

Reorder the terms:
-244 + 244 + 10X + X2 = 0 + 244

Combine like terms: -244 + 244 = 0
0 + 10X + X2 = 0 + 244
10X + X2 = 0 + 244

Combine like terms: 0 + 244 = 244
10X + X2 = 244

The X term is 10X.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10X + 25 + X2 = 244 + 25

Reorder the terms:
25 + 10X + X2 = 244 + 25

Combine like terms: 244 + 25 = 269
25 + 10X + X2 = 269

Factor a perfect square on the left side:
(X + 5)(X + 5) = 269

Calculate the square root of the right side: 16.401219467

Break this problem into two subproblems by setting 
(X + 5) equal to 16.401219467 and -16.401219467.


Subproblem 1
X + 5 = 16.401219467

Simplifying
X + 5 = 16.401219467

Reorder the terms:
5 + X = 16.401219467

Solving
5 + X = 16.401219467

Solving for variable 'X'.

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

Add '-5' to each side of the equation.
5 + -5 + X = 16.401219467 + -5

Combine like terms: 5 + -5 = 0
0 + X = 16.401219467 + -5
X = 16.401219467 + -5

Combine like terms: 16.401219467 + -5 = 11.401219467
X = 11.401219467

Simplifying
X = 11.401219467


Subproblem 2
X + 5 = -16.401219467

Simplifying
X + 5 = -16.401219467

Reorder the terms:
5 + X = -16.401219467

Solving
5 + X = -16.401219467

Solving for variable 'X'.

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

Add '-5' to each side of the equation.
5 + -5 + X = -16.401219467 + -5

Combine like terms: 5 + -5 = 0
0 + X = -16.401219467 + -5
X = -16.401219467 + -5

Combine like terms: -16.401219467 + -5 = -21.401219467
X = -21.401219467

Simplifying
X = -21.401219467


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {11.401219467, -21.401219467}

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