3x^2+30x-8400=0

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Solution for 3x^2+30x-8400=0 equation: 


Simplifying
3x2 + 30x + -8400 = 0

Reorder the terms:
-8400 + 30x + 3x2 = 0

Solving
-8400 + 30x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2800 + 10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2800 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-2800 + 10x + x2 = 0

Solving
-2800 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2800' to each side of the equation.
-2800 + 10x + 2800 + x2 = 0 + 2800

Reorder the terms:
-2800 + 2800 + 10x + x2 = 0 + 2800

Combine like terms: -2800 + 2800 = 0
0 + 10x + x2 = 0 + 2800
10x + x2 = 0 + 2800

Combine like terms: 0 + 2800 = 2800
10x + x2 = 2800

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 2800 + 25

Reorder the terms:
25 + 10x + x2 = 2800 + 25

Combine like terms: 2800 + 25 = 2825
25 + 10x + x2 = 2825

Factor a perfect square on the left side:
(x + 5)(x + 5) = 2825

Calculate the square root of the right side: 53.150729064

Break this problem into two subproblems by setting 
(x + 5) equal to 53.150729064 and -53.150729064.


Subproblem 1
x + 5 = 53.150729064

Simplifying
x + 5 = 53.150729064

Reorder the terms:
5 + x = 53.150729064

Solving
5 + x = 53.150729064

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 53.150729064 + -5

Combine like terms: 5 + -5 = 0
0 + x = 53.150729064 + -5
x = 53.150729064 + -5

Combine like terms: 53.150729064 + -5 = 48.150729064
x = 48.150729064

Simplifying
x = 48.150729064


Subproblem 2
x + 5 = -53.150729064

Simplifying
x + 5 = -53.150729064

Reorder the terms:
5 + x = -53.150729064

Solving
5 + x = -53.150729064

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -53.150729064 + -5

Combine like terms: 5 + -5 = 0
0 + x = -53.150729064 + -5
x = -53.150729064 + -5

Combine like terms: -53.150729064 + -5 = -58.150729064
x = -58.150729064

Simplifying
x = -58.150729064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.150729064, -58.150729064}
Solution
x = {48.150729064, -58.150729064}

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