z^2+18z+70=0

Solution for z^2+18z+70=0 equation:

Simplifying
z2 + 18z + 70 = 0

Reorder the terms:
70 + 18z + z2 = 0

Solving
70 + 18z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-70' to each side of the equation.
70 + 18z + -70 + z2 = 0 + -70

Reorder the terms:
70 + -70 + 18z + z2 = 0 + -70

Combine like terms: 70 + -70 = 0
0 + 18z + z2 = 0 + -70
18z + z2 = 0 + -70

Combine like terms: 0 + -70 = -70
18z + z2 = -70

The z term is 18z.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18z + 81 + z2 = -70 + 81

Reorder the terms:
81 + 18z + z2 = -70 + 81

Combine like terms: -70 + 81 = 11
81 + 18z + z2 = 11

Factor a perfect square on the left side:
(z + 9)(z + 9) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(z + 9) equal to 3.31662479 and -3.31662479.

Subproblem 1
z + 9 = 3.31662479

Simplifying
z + 9 = 3.31662479

Reorder the terms:
9 + z = 3.31662479

Solving
9 + z = 3.31662479

Solving for variable 'z'.

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

Add '-9' to each side of the equation.
9 + -9 + z = 3.31662479 + -9

Combine like terms: 9 + -9 = 0
0 + z = 3.31662479 + -9
z = 3.31662479 + -9

Combine like terms: 3.31662479 + -9 = -5.68337521
z = -5.68337521

Simplifying
z = -5.68337521

Subproblem 2
z + 9 = -3.31662479

Simplifying
z + 9 = -3.31662479

Reorder the terms:
9 + z = -3.31662479

Solving
9 + z = -3.31662479

Solving for variable 'z'.

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

Add '-9' to each side of the equation.
9 + -9 + z = -3.31662479 + -9

Combine like terms: 9 + -9 = 0
0 + z = -3.31662479 + -9
z = -3.31662479 + -9

Combine like terms: -3.31662479 + -9 = -12.31662479
z = -12.31662479

Simplifying
z = -12.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-5.68337521, -12.31662479}