x^2+11x=-5.25

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Solution for x^2+11x=-5.25 equation: 


Simplifying
x2 + 11x = -5.25

Reorder the terms:
11x + x2 = -5.25

Solving
11x + x2 = -5.25

Solving for variable 'x'.

Reorder the terms:
5.25 + 11x + x2 = -5.25 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
5.25 + 11x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + 11x + -5.25 + x2 = 0.00 + -5.25

Reorder the terms:
5.25 + -5.25 + 11x + x2 = 0.00 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + 11x + x2 = 0.00 + -5.25
11x + x2 = 0.00 + -5.25

Combine like terms: 0.00 + -5.25 = -5.25
11x + x2 = -5.25

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 = -5.25 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -5.25 + 30.25

Combine like terms: -5.25 + 30.25 = 25
30.25 + 11x + x2 = 25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5 and -5.


Subproblem 1
x + 5.5 = 5

Simplifying
x + 5.5 = 5

Reorder the terms:
5.5 + x = 5

Solving
5.5 + x = 5

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 = 5 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 5 + -5.5
x = 5 + -5.5

Combine like terms: 5 + -5.5 = -0.5
x = -0.5

Simplifying
x = -0.5


Subproblem 2
x + 5.5 = -5

Simplifying
x + 5.5 = -5

Reorder the terms:
5.5 + x = -5

Solving
5.5 + x = -5

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 = -5 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -5 + -5.5
x = -5 + -5.5

Combine like terms: -5 + -5.5 = -10.5
x = -10.5

Simplifying
x = -10.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -10.5}

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