x^2+4.8x+5.75=0

Solution for x^2+4.8x+5.75=0 equation:

Simplifying
x2 + 4.8x + 5.75 = 0

Reorder the terms:
5.75 + 4.8x + x2 = 0

Solving
5.75 + 4.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5.75' to each side of the equation.
5.75 + 4.8x + -5.75 + x2 = 0 + -5.75

Reorder the terms:
5.75 + -5.75 + 4.8x + x2 = 0 + -5.75

Combine like terms: 5.75 + -5.75 = 0.00
0.00 + 4.8x + x2 = 0 + -5.75
4.8x + x2 = 0 + -5.75

Combine like terms: 0 + -5.75 = -5.75
4.8x + x2 = -5.75

The x term is 4.8x.  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
4.8x + 5.76 + x2 = -5.75 + 5.76

Reorder the terms:
5.76 + 4.8x + x2 = -5.75 + 5.76

Combine like terms: -5.75 + 5.76 = 0.01
5.76 + 4.8x + x2 = 0.01

Factor a perfect square on the left side:
(x + 2.4)(x + 2.4) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(x + 2.4) equal to 0.1 and -0.1.

Subproblem 1
x + 2.4 = 0.1

Simplifying
x + 2.4 = 0.1

Reorder the terms:
2.4 + x = 0.1

Solving
2.4 + x = 0.1

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = 0.1 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = 0.1 + -2.4
x = 0.1 + -2.4

Combine like terms: 0.1 + -2.4 = -2.3
x = -2.3

Simplifying
x = -2.3

Subproblem 2
x + 2.4 = -0.1

Simplifying
x + 2.4 = -0.1

Reorder the terms:
2.4 + x = -0.1

Solving
2.4 + x = -0.1

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = -0.1 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = -0.1 + -2.4
x = -0.1 + -2.4

Combine like terms: -0.1 + -2.4 = -2.5
x = -2.5

Simplifying
x = -2.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.3, -2.5}