x^2+11x+30.25=22.75

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Solution for x^2+11x+30.25=22.75 equation: 


Simplifying
x2 + 11x + 30.25 = 22.75

Reorder the terms:
30.25 + 11x + x2 = 22.75

Solving
30.25 + 11x + x2 = 22.75

Solving for variable 'x'.

Reorder the terms:
30.25 + -22.75 + 11x + x2 = 22.75 + -22.75

Combine like terms: 30.25 + -22.75 = 7.5
7.5 + 11x + x2 = 22.75 + -22.75

Combine like terms: 22.75 + -22.75 = 0.00
7.5 + 11x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + 11x + -7.5 + x2 = 0.00 + -7.5

Reorder the terms:
7.5 + -7.5 + 11x + x2 = 0.00 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + 11x + x2 = 0.00 + -7.5
11x + x2 = 0.00 + -7.5

Combine like terms: 0.00 + -7.5 = -7.5
11x + x2 = -7.5

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -7.5 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -7.5 + 30.25

Combine like terms: -7.5 + 30.25 = 22.75
30.25 + 11x + x2 = 22.75

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 22.75

Calculate the square root of the right side: 4.769696007

Break this problem into two subproblems by setting 
(x + 5.5) equal to 4.769696007 and -4.769696007.


Subproblem 1
x + 5.5 = 4.769696007

Simplifying
x + 5.5 = 4.769696007

Reorder the terms:
5.5 + x = 4.769696007

Solving
5.5 + x = 4.769696007

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 4.769696007 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 4.769696007 + -5.5
x = 4.769696007 + -5.5

Combine like terms: 4.769696007 + -5.5 = -0.730303993
x = -0.730303993

Simplifying
x = -0.730303993


Subproblem 2
x + 5.5 = -4.769696007

Simplifying
x + 5.5 = -4.769696007

Reorder the terms:
5.5 + x = -4.769696007

Solving
5.5 + x = -4.769696007

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -4.769696007 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -4.769696007 + -5.5
x = -4.769696007 + -5.5

Combine like terms: -4.769696007 + -5.5 = -10.269696007
x = -10.269696007

Simplifying
x = -10.269696007


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.730303993, -10.269696007}

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