3x^2-6x-3=300

Solution for 3x^2-6x-3=300 equation:

Simplifying
3x2 + -6x + -3 = 300

Reorder the terms:
-3 + -6x + 3x2 = 300

Solving
-3 + -6x + 3x2 = 300

Solving for variable 'x'.

Reorder the terms:
-3 + -300 + -6x + 3x2 = 300 + -300

Combine like terms: -3 + -300 = -303
-303 + -6x + 3x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-303 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-101 + -2x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-101 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-101 + -2x + x2 = 0

Solving
-101 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '101' to each side of the equation.
-101 + -2x + 101 + x2 = 0 + 101

Reorder the terms:
-101 + 101 + -2x + x2 = 0 + 101

Combine like terms: -101 + 101 = 0
0 + -2x + x2 = 0 + 101
-2x + x2 = 0 + 101

Combine like terms: 0 + 101 = 101
-2x + x2 = 101

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 101 + 1

Reorder the terms:
1 + -2x + x2 = 101 + 1

Combine like terms: 101 + 1 = 102
1 + -2x + x2 = 102

Factor a perfect square on the left side:
(x + -1)(x + -1) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(x + -1) equal to 10.099504938 and -10.099504938.

Subproblem 1
x + -1 = 10.099504938

Simplifying
x + -1 = 10.099504938

Reorder the terms:
-1 + x = 10.099504938

Solving
-1 + x = 10.099504938

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 10.099504938 + 1

Combine like terms: -1 + 1 = 0
0 + x = 10.099504938 + 1
x = 10.099504938 + 1

Combine like terms: 10.099504938 + 1 = 11.099504938
x = 11.099504938

Simplifying
x = 11.099504938

Subproblem 2
x + -1 = -10.099504938

Simplifying
x + -1 = -10.099504938

Reorder the terms:
-1 + x = -10.099504938

Solving
-1 + x = -10.099504938

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -10.099504938 + 1

Combine like terms: -1 + 1 = 0
0 + x = -10.099504938 + 1
x = -10.099504938 + 1

Combine like terms: -10.099504938 + 1 = -9.099504938
x = -9.099504938

Simplifying
x = -9.099504938

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.099504938, -9.099504938}
Solution
x = {11.099504938, -9.099504938}