(x+8.5)(4x+34)=195

Solution for (x+8.5)(4x+34)=195 equation:

Simplifying
(x + 8.5)(4x + 34) = 195

Reorder the terms:
(8.5 + x)(4x + 34) = 195

Reorder the terms:
(8.5 + x)(34 + 4x) = 195

Multiply (8.5 + x) * (34 + 4x)
(8.5(34 + 4x) + x(34 + 4x)) = 195
((34 * 8.5 + 4x * 8.5) + x(34 + 4x)) = 195
((289 + 34x) + x(34 + 4x)) = 195
(289 + 34x + (34 * x + 4x * x)) = 195
(289 + 34x + (34x + 4x2)) = 195

Combine like terms: 34x + 34x = 68x
(289 + 68x + 4x2) = 195

Solving
289 + 68x + 4x2 = 195

Solving for variable 'x'.

Reorder the terms:
289 + -195 + 68x + 4x2 = 195 + -195

Combine like terms: 289 + -195 = 94
94 + 68x + 4x2 = 195 + -195

Combine like terms: 195 + -195 = 0
94 + 68x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(47 + 34x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(47 + 34x + 2x2)' equal to zero and attempt to solve:

Simplifying
47 + 34x + 2x2 = 0

Solving
47 + 34x + 2x2 = 0

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

Divide each side by '2'.
23.5 + 17x + x2 = 0

Move the constant term to the right:

Add '-23.5' to each side of the equation.
23.5 + 17x + -23.5 + x2 = 0 + -23.5

Reorder the terms:
23.5 + -23.5 + 17x + x2 = 0 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + 17x + x2 = 0 + -23.5
17x + x2 = 0 + -23.5

Combine like terms: 0 + -23.5 = -23.5
17x + x2 = -23.5

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = -23.5 + 72.25

Reorder the terms:
72.25 + 17x + x2 = -23.5 + 72.25

Combine like terms: -23.5 + 72.25 = 48.75
72.25 + 17x + x2 = 48.75

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 48.75

Calculate the square root of the right side: 6.982120022

Break this problem into two subproblems by setting 
(x + 8.5) equal to 6.982120022 and -6.982120022.

Subproblem 1
x + 8.5 = 6.982120022

Simplifying
x + 8.5 = 6.982120022

Reorder the terms:
8.5 + x = 6.982120022

Solving
8.5 + x = 6.982120022

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 6.982120022 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 6.982120022 + -8.5
x = 6.982120022 + -8.5

Combine like terms: 6.982120022 + -8.5 = -1.517879978
x = -1.517879978

Simplifying
x = -1.517879978

Subproblem 2
x + 8.5 = -6.982120022

Simplifying
x + 8.5 = -6.982120022

Reorder the terms:
8.5 + x = -6.982120022

Solving
8.5 + x = -6.982120022

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = -6.982120022 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -6.982120022 + -8.5
x = -6.982120022 + -8.5

Combine like terms: -6.982120022 + -8.5 = -15.482120022
x = -15.482120022

Simplifying
x = -15.482120022

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.517879978, -15.482120022}
Solution
x = {-1.517879978, -15.482120022}