-6x^2-216x-600=0

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Solution for -6x^2-216x-600=0 equation: 


Simplifying
-6x2 + -216x + -600 = 0

Reorder the terms:
-600 + -216x + -6x2 = 0

Solving
-600 + -216x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-6'.
-6(100 + 36x + x2) = 0

Ignore the factor -6.

Subproblem 1
Set the factor '(100 + 36x + x2)' equal to zero and attempt to solve:

Simplifying
100 + 36x + x2 = 0

Solving
100 + 36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + 36x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + 36x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + 36x + x2 = 0 + -100
36x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
36x + x2 = -100

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = -100 + 324

Reorder the terms:
324 + 36x + x2 = -100 + 324

Combine like terms: -100 + 324 = 224
324 + 36x + x2 = 224

Factor a perfect square on the left side:
(x + 18)(x + 18) = 224

Calculate the square root of the right side: 14.966629547

Break this problem into two subproblems by setting 
(x + 18) equal to 14.966629547 and -14.966629547.


Subproblem 1
x + 18 = 14.966629547

Simplifying
x + 18 = 14.966629547

Reorder the terms:
18 + x = 14.966629547

Solving
18 + x = 14.966629547

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = 14.966629547 + -18

Combine like terms: 18 + -18 = 0
0 + x = 14.966629547 + -18
x = 14.966629547 + -18

Combine like terms: 14.966629547 + -18 = -3.033370453
x = -3.033370453

Simplifying
x = -3.033370453


Subproblem 2
x + 18 = -14.966629547

Simplifying
x + 18 = -14.966629547

Reorder the terms:
18 + x = -14.966629547

Solving
18 + x = -14.966629547

Solving for variable 'x'.

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

Add '-18' to each side of the equation.
18 + -18 + x = -14.966629547 + -18

Combine like terms: 18 + -18 = 0
0 + x = -14.966629547 + -18
x = -14.966629547 + -18

Combine like terms: -14.966629547 + -18 = -32.966629547
x = -32.966629547

Simplifying
x = -32.966629547


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.033370453, -32.966629547}
Solution
x = {-3.033370453, -32.966629547}

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