5x^2+48x+20=0

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Solution for 5x^2+48x+20=0 equation: 


Simplifying
5x2 + 48x + 20 = 0

Reorder the terms:
20 + 48x + 5x2 = 0

Solving
20 + 48x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
4 + 9.6x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 9.6x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 9.6x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9.6x + x2 = 0 + -4
9.6x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
9.6x + x2 = -4

The x term is 9.6x.  Take half its coefficient (4.8).
Square it (23.04) and add it to both sides.

Add '23.04' to each side of the equation.
9.6x + 23.04 + x2 = -4 + 23.04

Reorder the terms:
23.04 + 9.6x + x2 = -4 + 23.04

Combine like terms: -4 + 23.04 = 19.04
23.04 + 9.6x + x2 = 19.04

Factor a perfect square on the left side:
(x + 4.8)(x + 4.8) = 19.04

Calculate the square root of the right side: 4.363484846

Break this problem into two subproblems by setting 
(x + 4.8) equal to 4.363484846 and -4.363484846.


Subproblem 1
x + 4.8 = 4.363484846

Simplifying
x + 4.8 = 4.363484846

Reorder the terms:
4.8 + x = 4.363484846

Solving
4.8 + x = 4.363484846

Solving for variable 'x'.

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

Add '-4.8' to each side of the equation.
4.8 + -4.8 + x = 4.363484846 + -4.8

Combine like terms: 4.8 + -4.8 = 0.0
0.0 + x = 4.363484846 + -4.8
x = 4.363484846 + -4.8

Combine like terms: 4.363484846 + -4.8 = -0.436515154
x = -0.436515154

Simplifying
x = -0.436515154


Subproblem 2
x + 4.8 = -4.363484846

Simplifying
x + 4.8 = -4.363484846

Reorder the terms:
4.8 + x = -4.363484846

Solving
4.8 + x = -4.363484846

Solving for variable 'x'.

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

Add '-4.8' to each side of the equation.
4.8 + -4.8 + x = -4.363484846 + -4.8

Combine like terms: 4.8 + -4.8 = 0.0
0.0 + x = -4.363484846 + -4.8
x = -4.363484846 + -4.8

Combine like terms: -4.363484846 + -4.8 = -9.163484846
x = -9.163484846

Simplifying
x = -9.163484846


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.436515154, -9.163484846}

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