3x^2+600x=4800

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Solution for 3x^2+600x=4800 equation:


Simplifying
3x2 + 600x = 4800

Reorder the terms:
600x + 3x2 = 4800

Solving
600x + 3x2 = 4800

Solving for variable 'x'.

Reorder the terms:
-4800 + 600x + 3x2 = 4800 + -4800

Combine like terms: 4800 + -4800 = 0
-4800 + 600x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1600 + 200x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1600 + 200x + x2)' equal to zero and attempt to solve:

Simplifying
-1600 + 200x + x2 = 0

Solving
-1600 + 200x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1600' to each side of the equation.
-1600 + 200x + 1600 + x2 = 0 + 1600

Reorder the terms:
-1600 + 1600 + 200x + x2 = 0 + 1600

Combine like terms: -1600 + 1600 = 0
0 + 200x + x2 = 0 + 1600
200x + x2 = 0 + 1600

Combine like terms: 0 + 1600 = 1600
200x + x2 = 1600

The x term is 200x.  Take half its coefficient (100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
200x + 10000 + x2 = 1600 + 10000

Reorder the terms:
10000 + 200x + x2 = 1600 + 10000

Combine like terms: 1600 + 10000 = 11600
10000 + 200x + x2 = 11600

Factor a perfect square on the left side:
(x + 100)(x + 100) = 11600

Calculate the square root of the right side: 107.703296143

Break this problem into two subproblems by setting 
(x + 100) equal to 107.703296143 and -107.703296143.


Subproblem 1
x + 100 = 107.703296143

Simplifying
x + 100 = 107.703296143

Reorder the terms:
100 + x = 107.703296143

Solving
100 + x = 107.703296143

Solving for variable 'x'.

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

Add '-100' to each side of the equation.
100 + -100 + x = 107.703296143 + -100

Combine like terms: 100 + -100 = 0
0 + x = 107.703296143 + -100
x = 107.703296143 + -100

Combine like terms: 107.703296143 + -100 = 7.703296143
x = 7.703296143

Simplifying
x = 7.703296143


Subproblem 2
x + 100 = -107.703296143

Simplifying
x + 100 = -107.703296143

Reorder the terms:
100 + x = -107.703296143

Solving
100 + x = -107.703296143

Solving for variable 'x'.

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

Add '-100' to each side of the equation.
100 + -100 + x = -107.703296143 + -100

Combine like terms: 100 + -100 = 0
0 + x = -107.703296143 + -100
x = -107.703296143 + -100

Combine like terms: -107.703296143 + -100 = -207.703296143
x = -207.703296143

Simplifying
x = -207.703296143


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.703296143, -207.703296143}
Solution
x = {7.703296143, -207.703296143}

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