2x^2+74x+210=0

Solution for 2x^2+74x+210=0 equation:

Simplifying
2x2 + 74x + 210 = 0

Reorder the terms:
210 + 74x + 2x2 = 0

Solving
210 + 74x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(105 + 37x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(105 + 37x + x2)' equal to zero and attempt to solve:

Simplifying
105 + 37x + x2 = 0

Solving
105 + 37x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-105' to each side of the equation.
105 + 37x + -105 + x2 = 0 + -105

Reorder the terms:
105 + -105 + 37x + x2 = 0 + -105

Combine like terms: 105 + -105 = 0
0 + 37x + x2 = 0 + -105
37x + x2 = 0 + -105

Combine like terms: 0 + -105 = -105
37x + x2 = -105

The x term is 37x.  Take half its coefficient (18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
37x + 342.25 + x2 = -105 + 342.25

Reorder the terms:
342.25 + 37x + x2 = -105 + 342.25

Combine like terms: -105 + 342.25 = 237.25
342.25 + 37x + x2 = 237.25

Factor a perfect square on the left side:
(x + 18.5)(x + 18.5) = 237.25

Calculate the square root of the right side: 15.402921801

Break this problem into two subproblems by setting 
(x + 18.5) equal to 15.402921801 and -15.402921801.

Subproblem 1
x + 18.5 = 15.402921801

Simplifying
x + 18.5 = 15.402921801

Reorder the terms:
18.5 + x = 15.402921801

Solving
18.5 + x = 15.402921801

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = 15.402921801 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = 15.402921801 + -18.5
x = 15.402921801 + -18.5

Combine like terms: 15.402921801 + -18.5 = -3.097078199
x = -3.097078199

Simplifying
x = -3.097078199

Subproblem 2
x + 18.5 = -15.402921801

Simplifying
x + 18.5 = -15.402921801

Reorder the terms:
18.5 + x = -15.402921801

Solving
18.5 + x = -15.402921801

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = -15.402921801 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = -15.402921801 + -18.5
x = -15.402921801 + -18.5

Combine like terms: -15.402921801 + -18.5 = -33.902921801
x = -33.902921801

Simplifying
x = -33.902921801

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.097078199, -33.902921801}
Solution
x = {-3.097078199, -33.902921801}