2z^2+17z+10=0

Solution for 2z^2+17z+10=0 equation:

Simplifying
2z2 + 17z + 10 = 0

Reorder the terms:
10 + 17z + 2z2 = 0

Solving
10 + 17z + 2z2 = 0

Solving for variable 'z'.

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

Divide each side by '2'.
5 + 8.5z + z2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 8.5z + -5 + z2 = 0 + -5

Reorder the terms:
5 + -5 + 8.5z + z2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8.5z + z2 = 0 + -5
8.5z + z2 = 0 + -5

Combine like terms: 0 + -5 = -5
8.5z + z2 = -5

The z term is 8.5z.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5z + 18.0625 + z2 = -5 + 18.0625

Reorder the terms:
18.0625 + 8.5z + z2 = -5 + 18.0625

Combine like terms: -5 + 18.0625 = 13.0625
18.0625 + 8.5z + z2 = 13.0625

Factor a perfect square on the left side:
(z + 4.25)(z + 4.25) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(z + 4.25) equal to 3.614208074 and -3.614208074.

Subproblem 1
z + 4.25 = 3.614208074

Simplifying
z + 4.25 = 3.614208074

Reorder the terms:
4.25 + z = 3.614208074

Solving
4.25 + z = 3.614208074

Solving for variable 'z'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + z = 3.614208074 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + z = 3.614208074 + -4.25
z = 3.614208074 + -4.25

Combine like terms: 3.614208074 + -4.25 = -0.635791926
z = -0.635791926

Simplifying
z = -0.635791926

Subproblem 2
z + 4.25 = -3.614208074

Simplifying
z + 4.25 = -3.614208074

Reorder the terms:
4.25 + z = -3.614208074

Solving
4.25 + z = -3.614208074

Solving for variable 'z'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + z = -3.614208074 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + z = -3.614208074 + -4.25
z = -3.614208074 + -4.25

Combine like terms: -3.614208074 + -4.25 = -7.864208074
z = -7.864208074

Simplifying
z = -7.864208074

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-0.635791926, -7.864208074}