x^2+9x+20.25=136+2-.25

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Solution for x^2+9x+20.25=136+2-.25 equation: 


Simplifying
x2 + 9x + 20.25 = 136 + 2 + -0.25

Reorder the terms:
20.25 + 9x + x2 = 136 + 2 + -0.25

Combine like terms: 136 + 2 = 138
20.25 + 9x + x2 = 138 + -0.25

Combine like terms: 138 + -0.25 = 137.75
20.25 + 9x + x2 = 137.75

Solving
20.25 + 9x + x2 = 137.75

Solving for variable 'x'.

Reorder the terms:
20.25 + -137.75 + 9x + x2 = 137.75 + -137.75

Combine like terms: 20.25 + -137.75 = -117.5
-117.5 + 9x + x2 = 137.75 + -137.75

Combine like terms: 137.75 + -137.75 = 0.00
-117.5 + 9x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '117.5' to each side of the equation.
-117.5 + 9x + 117.5 + x2 = 0.00 + 117.5

Reorder the terms:
-117.5 + 117.5 + 9x + x2 = 0.00 + 117.5

Combine like terms: -117.5 + 117.5 = 0.0
0.0 + 9x + x2 = 0.00 + 117.5
9x + x2 = 0.00 + 117.5

Combine like terms: 0.00 + 117.5 = 117.5
9x + x2 = 117.5

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 = 117.5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 117.5 + 20.25

Combine like terms: 117.5 + 20.25 = 137.75
20.25 + 9x + x2 = 137.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 137.75

Calculate the square root of the right side: 11.736694594

Break this problem into two subproblems by setting 
(x + 4.5) equal to 11.736694594 and -11.736694594.


Subproblem 1
x + 4.5 = 11.736694594

Simplifying
x + 4.5 = 11.736694594

Reorder the terms:
4.5 + x = 11.736694594

Solving
4.5 + x = 11.736694594

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 = 11.736694594 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 11.736694594 + -4.5
x = 11.736694594 + -4.5

Combine like terms: 11.736694594 + -4.5 = 7.236694594
x = 7.236694594

Simplifying
x = 7.236694594


Subproblem 2
x + 4.5 = -11.736694594

Simplifying
x + 4.5 = -11.736694594

Reorder the terms:
4.5 + x = -11.736694594

Solving
4.5 + x = -11.736694594

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 = -11.736694594 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -11.736694594 + -4.5
x = -11.736694594 + -4.5

Combine like terms: -11.736694594 + -4.5 = -16.236694594
x = -16.236694594

Simplifying
x = -16.236694594


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.236694594, -16.236694594}

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