0=x^2+10x+8

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


Simplifying
0 = x2 + 10x + 8

Reorder the terms:
0 = 8 + 10x + x2

Solving
0 = 8 + 10x + x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -10x + -1x2 = 8 + 10x + x2 + -8 + -10x + -1x2

Reorder the terms:
-8 + -10x + -1x2 = 8 + -8 + 10x + -10x + x2 + -1x2

Combine like terms: 8 + -8 = 0
-8 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2
-8 + -10x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-8 + -10x + -1x2 = 0 + x2 + -1x2
-8 + -10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -10x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 10x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
8 + 10x + x2 = 0

Solving
8 + 10x + x2 = 0

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}
Solution
x = {-0.876894374, -9.123105626}

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