5x(5x+4)=120

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Solution for 5x(5x+4)=120 equation: 


Simplifying
5x(5x + 4) = 120

Reorder the terms:
5x(4 + 5x) = 120
(4 * 5x + 5x * 5x) = 120
(20x + 25x2) = 120

Solving
20x + 25x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 20x + 25x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 20x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + 4x + 5x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-24 + 4x + 5x2)' equal to zero and attempt to solve:

Simplifying
-24 + 4x + 5x2 = 0

Solving
-24 + 4x + 5x2 = 0

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

Divide each side by '5'.
-4.8 + 0.8x + x2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + 0.8x + 4.8 + x2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + 0.8x + x2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + 0.8x + x2 = 0 + 4.8
0.8x + x2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
0.8x + x2 = 4.8

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 4.8 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 4.8 + 0.16

Combine like terms: 4.8 + 0.16 = 4.96
0.16 + 0.8x + x2 = 4.96

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 4.96

Calculate the square root of the right side: 2.227105745

Break this problem into two subproblems by setting 
(x + 0.4) equal to 2.227105745 and -2.227105745.


Subproblem 1
x + 0.4 = 2.227105745

Simplifying
x + 0.4 = 2.227105745

Reorder the terms:
0.4 + x = 2.227105745

Solving
0.4 + x = 2.227105745

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 2.227105745 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 2.227105745 + -0.4
x = 2.227105745 + -0.4

Combine like terms: 2.227105745 + -0.4 = 1.827105745
x = 1.827105745

Simplifying
x = 1.827105745


Subproblem 2
x + 0.4 = -2.227105745

Simplifying
x + 0.4 = -2.227105745

Reorder the terms:
0.4 + x = -2.227105745

Solving
0.4 + x = -2.227105745

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -2.227105745 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -2.227105745 + -0.4
x = -2.227105745 + -0.4

Combine like terms: -2.227105745 + -0.4 = -2.627105745
x = -2.627105745

Simplifying
x = -2.627105745


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.827105745, -2.627105745}
Solution
x = {1.827105745, -2.627105745}

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