X^2+10X+8=0

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Solution for X^2+10X+8=0 equation: 


Simplifying
X2 + 10X + 8 = 0

Reorder the terms:
8 + 10X + X2 = 0

Solving
8 + 10X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 10X + -8 + X2 = 0 + -8

Reorder the terms:
8 + -8 + 10X + X2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 10X + X2 = 0 + -8
10X + X2 = 0 + -8

Combine like terms: 0 + -8 = -8
10X + X2 = -8

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 = -8 + 25

Reorder the terms:
25 + 10X + X2 = -8 + 25

Combine like terms: -8 + 25 = 17
25 + 10X + X2 = 17

Factor a perfect square on the left side:
(X + 5)(X + 5) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(X + 5) equal to 4.123105626 and -4.123105626.


Subproblem 1
X + 5 = 4.123105626

Simplifying
X + 5 = 4.123105626

Reorder the terms:
5 + X = 4.123105626

Solving
5 + X = 4.123105626

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 = 4.123105626 + -5

Combine like terms: 5 + -5 = 0
0 + X = 4.123105626 + -5
X = 4.123105626 + -5

Combine like terms: 4.123105626 + -5 = -0.876894374
X = -0.876894374

Simplifying
X = -0.876894374


Subproblem 2
X + 5 = -4.123105626

Simplifying
X + 5 = -4.123105626

Reorder the terms:
5 + X = -4.123105626

Solving
5 + X = -4.123105626

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 = -4.123105626 + -5

Combine like terms: 5 + -5 = 0
0 + X = -4.123105626 + -5
X = -4.123105626 + -5

Combine like terms: -4.123105626 + -5 = -9.123105626
X = -9.123105626

Simplifying
X = -9.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-0.876894374, -9.123105626}

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