x^2+5x+5.25=0

Solution for x^2+5x+5.25=0 equation:

Simplifying
x2 + 5x + 5.25 = 0

Reorder the terms:
5.25 + 5x + x2 = 0

Solving
5.25 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + 5x + -5.25 + x2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + 5x + x2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + 5x + x2 = 0 + -5.25
5x + x2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
5x + x2 = -5.25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -5.25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -5.25 + 6.25

Combine like terms: -5.25 + 6.25 = 1
6.25 + 5x + x2 = 1

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1 and -1.

Subproblem 1
x + 2.5 = 1

Simplifying
x + 2.5 = 1

Reorder the terms:
2.5 + x = 1

Solving
2.5 + x = 1

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1 + -2.5
x = 1 + -2.5

Combine like terms: 1 + -2.5 = -1.5
x = -1.5

Simplifying
x = -1.5

Subproblem 2
x + 2.5 = -1

Simplifying
x + 2.5 = -1

Reorder the terms:
2.5 + x = -1

Solving
2.5 + x = -1

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1 + -2.5
x = -1 + -2.5

Combine like terms: -1 + -2.5 = -3.5
x = -3.5

Simplifying
x = -3.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.5, -3.5}