(z+5)(z+5)=10

Solution for (z+5)(z+5)=10 equation:

Simplifying
(z + 5)(z + 5) = 10

Reorder the terms:
(5 + z)(z + 5) = 10

Reorder the terms:
(5 + z)(5 + z) = 10

Multiply (5 + z) * (5 + z)
(5(5 + z) + z(5 + z)) = 10
((5 * 5 + z * 5) + z(5 + z)) = 10
((25 + 5z) + z(5 + z)) = 10
(25 + 5z + (5 * z + z * z)) = 10
(25 + 5z + (5z + z2)) = 10

Combine like terms: 5z + 5z = 10z
(25 + 10z + z2) = 10

Solving
25 + 10z + z2 = 10

Solving for variable 'z'.

Reorder the terms:
25 + -10 + 10z + z2 = 10 + -10

Combine like terms: 25 + -10 = 15
15 + 10z + z2 = 10 + -10

Combine like terms: 10 + -10 = 0
15 + 10z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 10z + -15 + z2 = 0 + -15

Reorder the terms:
15 + -15 + 10z + z2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 10z + z2 = 0 + -15
10z + z2 = 0 + -15

Combine like terms: 0 + -15 = -15
10z + z2 = -15

The z term is 10z.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10z + 25 + z2 = -15 + 25

Reorder the terms:
25 + 10z + z2 = -15 + 25

Combine like terms: -15 + 25 = 10
25 + 10z + z2 = 10

Factor a perfect square on the left side:
(z + 5)(z + 5) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(z + 5) equal to 3.16227766 and -3.16227766.

Subproblem 1
z + 5 = 3.16227766

Simplifying
z + 5 = 3.16227766

Reorder the terms:
5 + z = 3.16227766

Solving
5 + z = 3.16227766

Solving for variable 'z'.

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

Add '-5' to each side of the equation.
5 + -5 + z = 3.16227766 + -5

Combine like terms: 5 + -5 = 0
0 + z = 3.16227766 + -5
z = 3.16227766 + -5

Combine like terms: 3.16227766 + -5 = -1.83772234
z = -1.83772234

Simplifying
z = -1.83772234

Subproblem 2
z + 5 = -3.16227766

Simplifying
z + 5 = -3.16227766

Reorder the terms:
5 + z = -3.16227766

Solving
5 + z = -3.16227766

Solving for variable 'z'.

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

Add '-5' to each side of the equation.
5 + -5 + z = -3.16227766 + -5

Combine like terms: 5 + -5 = 0
0 + z = -3.16227766 + -5
z = -3.16227766 + -5

Combine like terms: -3.16227766 + -5 = -8.16227766
z = -8.16227766

Simplifying
z = -8.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-1.83772234, -8.16227766}