2x^2+21x-85=0

Solution for 2x^2+21x-85=0 equation:

Simplifying
2x2 + 21x + -85 = 0

Reorder the terms:
-85 + 21x + 2x2 = 0

Solving
-85 + 21x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-42.5 + 10.5x + x2 = 0

Move the constant term to the right:

Add '42.5' to each side of the equation.
-42.5 + 10.5x + 42.5 + x2 = 0 + 42.5

Reorder the terms:
-42.5 + 42.5 + 10.5x + x2 = 0 + 42.5

Combine like terms: -42.5 + 42.5 = 0.0
0.0 + 10.5x + x2 = 0 + 42.5
10.5x + x2 = 0 + 42.5

Combine like terms: 0 + 42.5 = 42.5
10.5x + x2 = 42.5

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = 42.5 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = 42.5 + 27.5625

Combine like terms: 42.5 + 27.5625 = 70.0625
27.5625 + 10.5x + x2 = 70.0625

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 70.0625

Calculate the square root of the right side: 8.370334521

Break this problem into two subproblems by setting 
(x + 5.25) equal to 8.370334521 and -8.370334521.

Subproblem 1
x + 5.25 = 8.370334521

Simplifying
x + 5.25 = 8.370334521

Reorder the terms:
5.25 + x = 8.370334521

Solving
5.25 + x = 8.370334521

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = 8.370334521 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = 8.370334521 + -5.25
x = 8.370334521 + -5.25

Combine like terms: 8.370334521 + -5.25 = 3.120334521
x = 3.120334521

Simplifying
x = 3.120334521

Subproblem 2
x + 5.25 = -8.370334521

Simplifying
x + 5.25 = -8.370334521

Reorder the terms:
5.25 + x = -8.370334521

Solving
5.25 + x = -8.370334521

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = -8.370334521 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = -8.370334521 + -5.25
x = -8.370334521 + -5.25

Combine like terms: -8.370334521 + -5.25 = -13.620334521
x = -13.620334521

Simplifying
x = -13.620334521

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.120334521, -13.620334521}