0=x^2+9x+5

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Solution for 0=x^2+9x+5 equation:


Simplifying
0 = x2 + 9x + 5

Reorder the terms:
0 = 5 + 9x + x2

Solving
0 = 5 + 9x + x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -9x + -1x2 = 5 + 9x + x2 + -5 + -9x + -1x2

Reorder the terms:
-5 + -9x + -1x2 = 5 + -5 + 9x + -9x + x2 + -1x2

Combine like terms: 5 + -5 = 0
-5 + -9x + -1x2 = 0 + 9x + -9x + x2 + -1x2
-5 + -9x + -1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
-5 + -9x + -1x2 = 0 + x2 + -1x2
-5 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + -9x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 9x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 9x + x2 = 0

Solving
5 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 9x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 9x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9x + x2 = 0 + -5
9x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
9x + x2 = -5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -5 + 20.25

Combine like terms: -5 + 20.25 = 15.25
20.25 + 9x + x2 = 15.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
x + 4.5 = 3.905124838

Simplifying
x + 4.5 = 3.905124838

Reorder the terms:
4.5 + x = 3.905124838

Solving
4.5 + x = 3.905124838

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 3.905124838 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 3.905124838 + -4.5
x = 3.905124838 + -4.5

Combine like terms: 3.905124838 + -4.5 = -0.594875162
x = -0.594875162

Simplifying
x = -0.594875162


Subproblem 2
x + 4.5 = -3.905124838

Simplifying
x + 4.5 = -3.905124838

Reorder the terms:
4.5 + x = -3.905124838

Solving
4.5 + x = -3.905124838

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -3.905124838 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -3.905124838 + -4.5
x = -3.905124838 + -4.5

Combine like terms: -3.905124838 + -4.5 = -8.405124838
x = -8.405124838

Simplifying
x = -8.405124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.594875162, -8.405124838}
Solution
x = {-0.594875162, -8.405124838}

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