5x^2+960x+14400=0

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Solution for 5x^2+960x+14400=0 equation: 


Simplifying
5x2 + 960x + 14400 = 0

Reorder the terms:
14400 + 960x + 5x2 = 0

Solving
14400 + 960x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2880 + 192x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2880 + 192x + x2)' equal to zero and attempt to solve:

Simplifying
2880 + 192x + x2 = 0

Solving
2880 + 192x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2880' to each side of the equation.
2880 + 192x + -2880 + x2 = 0 + -2880

Reorder the terms:
2880 + -2880 + 192x + x2 = 0 + -2880

Combine like terms: 2880 + -2880 = 0
0 + 192x + x2 = 0 + -2880
192x + x2 = 0 + -2880

Combine like terms: 0 + -2880 = -2880
192x + x2 = -2880

The x term is 192x.  Take half its coefficient (96).
Square it (9216) and add it to both sides.

Add '9216' to each side of the equation.
192x + 9216 + x2 = -2880 + 9216

Reorder the terms:
9216 + 192x + x2 = -2880 + 9216

Combine like terms: -2880 + 9216 = 6336
9216 + 192x + x2 = 6336

Factor a perfect square on the left side:
(x + 96)(x + 96) = 6336

Calculate the square root of the right side: 79.598994969

Break this problem into two subproblems by setting 
(x + 96) equal to 79.598994969 and -79.598994969.


Subproblem 1
x + 96 = 79.598994969

Simplifying
x + 96 = 79.598994969

Reorder the terms:
96 + x = 79.598994969

Solving
96 + x = 79.598994969

Solving for variable 'x'.

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

Add '-96' to each side of the equation.
96 + -96 + x = 79.598994969 + -96

Combine like terms: 96 + -96 = 0
0 + x = 79.598994969 + -96
x = 79.598994969 + -96

Combine like terms: 79.598994969 + -96 = -16.401005031
x = -16.401005031

Simplifying
x = -16.401005031


Subproblem 2
x + 96 = -79.598994969

Simplifying
x + 96 = -79.598994969

Reorder the terms:
96 + x = -79.598994969

Solving
96 + x = -79.598994969

Solving for variable 'x'.

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

Add '-96' to each side of the equation.
96 + -96 + x = -79.598994969 + -96

Combine like terms: 96 + -96 = 0
0 + x = -79.598994969 + -96
x = -79.598994969 + -96

Combine like terms: -79.598994969 + -96 = -175.598994969
x = -175.598994969

Simplifying
x = -175.598994969


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-16.401005031, -175.598994969}
Solution
x = {-16.401005031, -175.598994969}

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