3x^2-210x+49=0

Solution for 3x^2-210x+49=0 equation:

Simplifying
3x2 + -210x + 49 = 0

Reorder the terms:
49 + -210x + 3x2 = 0

Solving
49 + -210x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
16.33333333 + -70x + x2 = 0

Move the constant term to the right:

Add '-16.33333333' to each side of the equation.
16.33333333 + -70x + -16.33333333 + x2 = 0 + -16.33333333

Reorder the terms:
16.33333333 + -16.33333333 + -70x + x2 = 0 + -16.33333333

Combine like terms: 16.33333333 + -16.33333333 = 0.00000000
0.00000000 + -70x + x2 = 0 + -16.33333333
-70x + x2 = 0 + -16.33333333

Combine like terms: 0 + -16.33333333 = -16.33333333
-70x + x2 = -16.33333333

The x term is -70x.  Take half its coefficient (-35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
-70x + 1225 + x2 = -16.33333333 + 1225

Reorder the terms:
1225 + -70x + x2 = -16.33333333 + 1225

Combine like terms: -16.33333333 + 1225 = 1208.66666667
1225 + -70x + x2 = 1208.66666667

Factor a perfect square on the left side:
(x + -35)(x + -35) = 1208.66666667

Calculate the square root of the right side: 34.76588366

Break this problem into two subproblems by setting 
(x + -35) equal to 34.76588366 and -34.76588366.

Subproblem 1
x + -35 = 34.76588366

Simplifying
x + -35 = 34.76588366

Reorder the terms:
-35 + x = 34.76588366

Solving
-35 + x = 34.76588366

Solving for variable 'x'.

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

Add '35' to each side of the equation.
-35 + 35 + x = 34.76588366 + 35

Combine like terms: -35 + 35 = 0
0 + x = 34.76588366 + 35
x = 34.76588366 + 35

Combine like terms: 34.76588366 + 35 = 69.76588366
x = 69.76588366

Simplifying
x = 69.76588366

Subproblem 2
x + -35 = -34.76588366

Simplifying
x + -35 = -34.76588366

Reorder the terms:
-35 + x = -34.76588366

Solving
-35 + x = -34.76588366

Solving for variable 'x'.

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

Add '35' to each side of the equation.
-35 + 35 + x = -34.76588366 + 35

Combine like terms: -35 + 35 = 0
0 + x = -34.76588366 + 35
x = -34.76588366 + 35

Combine like terms: -34.76588366 + 35 = 0.23411634
x = 0.23411634

Simplifying
x = 0.23411634

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {69.76588366, 0.23411634}