3x^2-792x+2100=0

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Solution for 3x^2-792x+2100=0 equation: 


Simplifying
3x2 + -792x + 2100 = 0

Reorder the terms:
2100 + -792x + 3x2 = 0

Solving
2100 + -792x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(700 + -264x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(700 + -264x + x2)' equal to zero and attempt to solve:

Simplifying
700 + -264x + x2 = 0

Solving
700 + -264x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-700' to each side of the equation.
700 + -264x + -700 + x2 = 0 + -700

Reorder the terms:
700 + -700 + -264x + x2 = 0 + -700

Combine like terms: 700 + -700 = 0
0 + -264x + x2 = 0 + -700
-264x + x2 = 0 + -700

Combine like terms: 0 + -700 = -700
-264x + x2 = -700

The x term is -264x.  Take half its coefficient (-132).
Square it (17424) and add it to both sides.

Add '17424' to each side of the equation.
-264x + 17424 + x2 = -700 + 17424

Reorder the terms:
17424 + -264x + x2 = -700 + 17424

Combine like terms: -700 + 17424 = 16724
17424 + -264x + x2 = 16724

Factor a perfect square on the left side:
(x + -132)(x + -132) = 16724

Calculate the square root of the right side: 129.321305283

Break this problem into two subproblems by setting 
(x + -132) equal to 129.321305283 and -129.321305283.


Subproblem 1
x + -132 = 129.321305283

Simplifying
x + -132 = 129.321305283

Reorder the terms:
-132 + x = 129.321305283

Solving
-132 + x = 129.321305283

Solving for variable 'x'.

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

Add '132' to each side of the equation.
-132 + 132 + x = 129.321305283 + 132

Combine like terms: -132 + 132 = 0
0 + x = 129.321305283 + 132
x = 129.321305283 + 132

Combine like terms: 129.321305283 + 132 = 261.321305283
x = 261.321305283

Simplifying
x = 261.321305283


Subproblem 2
x + -132 = -129.321305283

Simplifying
x + -132 = -129.321305283

Reorder the terms:
-132 + x = -129.321305283

Solving
-132 + x = -129.321305283

Solving for variable 'x'.

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

Add '132' to each side of the equation.
-132 + 132 + x = -129.321305283 + 132

Combine like terms: -132 + 132 = 0
0 + x = -129.321305283 + 132
x = -129.321305283 + 132

Combine like terms: -129.321305283 + 132 = 2.678694717
x = 2.678694717

Simplifying
x = 2.678694717


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {261.321305283, 2.678694717}
Solution
x = {261.321305283, 2.678694717}

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