x^2+6x+2.4=0

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Solution for x^2+6x+2.4=0 equation: 


Simplifying
x2 + 6x + 2.4 = 0

Reorder the terms:
2.4 + 6x + x2 = 0

Solving
2.4 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + 6x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + 6x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + 6x + x2 = 0 + -2.4
6x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
6x + x2 = -2.4

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -2.4 + 9

Reorder the terms:
9 + 6x + x2 = -2.4 + 9

Combine like terms: -2.4 + 9 = 6.6
9 + 6x + x2 = 6.6

Factor a perfect square on the left side:
(x + 3)(x + 3) = 6.6

Calculate the square root of the right side: 2.569046516

Break this problem into two subproblems by setting 
(x + 3) equal to 2.569046516 and -2.569046516.


Subproblem 1
x + 3 = 2.569046516

Simplifying
x + 3 = 2.569046516

Reorder the terms:
3 + x = 2.569046516

Solving
3 + x = 2.569046516

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.569046516 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.569046516 + -3
x = 2.569046516 + -3

Combine like terms: 2.569046516 + -3 = -0.430953484
x = -0.430953484

Simplifying
x = -0.430953484


Subproblem 2
x + 3 = -2.569046516

Simplifying
x + 3 = -2.569046516

Reorder the terms:
3 + x = -2.569046516

Solving
3 + x = -2.569046516

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.569046516 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.569046516 + -3
x = -2.569046516 + -3

Combine like terms: -2.569046516 + -3 = -5.569046516
x = -5.569046516

Simplifying
x = -5.569046516


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.430953484, -5.569046516}

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