(Z+5)(Z+5)=7

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Solution for (Z+5)(Z+5)=7 equation: 


Simplifying
(Z + 5)(Z + 5) = 7

Reorder the terms:
(5 + Z)(Z + 5) = 7

Reorder the terms:
(5 + Z)(5 + Z) = 7

Multiply (5 + Z) * (5 + Z)
(5(5 + Z) + Z(5 + Z)) = 7
((5 * 5 + Z * 5) + Z(5 + Z)) = 7
((25 + 5Z) + Z(5 + Z)) = 7
(25 + 5Z + (5 * Z + Z * Z)) = 7
(25 + 5Z + (5Z + Z2)) = 7

Combine like terms: 5Z + 5Z = 10Z
(25 + 10Z + Z2) = 7

Solving
25 + 10Z + Z2 = 7

Solving for variable 'Z'.

Reorder the terms:
25 + -7 + 10Z + Z2 = 7 + -7

Combine like terms: 25 + -7 = 18
18 + 10Z + Z2 = 7 + -7

Combine like terms: 7 + -7 = 0
18 + 10Z + Z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 10Z + -18 + Z2 = 0 + -18

Reorder the terms:
18 + -18 + 10Z + Z2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 10Z + Z2 = 0 + -18
10Z + Z2 = 0 + -18

Combine like terms: 0 + -18 = -18
10Z + Z2 = -18

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 = -18 + 25

Reorder the terms:
25 + 10Z + Z2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + 10Z + Z2 = 7

Factor a perfect square on the left side:
(Z + 5)(Z + 5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(Z + 5) equal to 2.645751311 and -2.645751311.


Subproblem 1
Z + 5 = 2.645751311

Simplifying
Z + 5 = 2.645751311

Reorder the terms:
5 + Z = 2.645751311

Solving
5 + Z = 2.645751311

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 = 2.645751311 + -5

Combine like terms: 5 + -5 = 0
0 + Z = 2.645751311 + -5
Z = 2.645751311 + -5

Combine like terms: 2.645751311 + -5 = -2.354248689
Z = -2.354248689

Simplifying
Z = -2.354248689


Subproblem 2
Z + 5 = -2.645751311

Simplifying
Z + 5 = -2.645751311

Reorder the terms:
5 + Z = -2.645751311

Solving
5 + Z = -2.645751311

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 = -2.645751311 + -5

Combine like terms: 5 + -5 = 0
0 + Z = -2.645751311 + -5
Z = -2.645751311 + -5

Combine like terms: -2.645751311 + -5 = -7.645751311
Z = -7.645751311

Simplifying
Z = -7.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
Z = {-2.354248689, -7.645751311}

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