z^2-14z=-42

Solution for z^2-14z=-42 equation:

Simplifying
z2 + -14z = -42

Reorder the terms:
-14z + z2 = -42

Solving
-14z + z2 = -42

Solving for variable 'z'.

Reorder the terms:
42 + -14z + z2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + -14z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -14z + -42 + z2 = 0 + -42

Reorder the terms:
42 + -42 + -14z + z2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -14z + z2 = 0 + -42
-14z + z2 = 0 + -42

Combine like terms: 0 + -42 = -42
-14z + z2 = -42

The z term is -14z.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14z + 49 + z2 = -42 + 49

Reorder the terms:
49 + -14z + z2 = -42 + 49

Combine like terms: -42 + 49 = 7
49 + -14z + z2 = 7

Factor a perfect square on the left side:
(z + -7)(z + -7) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(z + -7) equal to 2.645751311 and -2.645751311.

Subproblem 1
z + -7 = 2.645751311

Simplifying
z + -7 = 2.645751311

Reorder the terms:
-7 + z = 2.645751311

Solving
-7 + z = 2.645751311

Solving for variable 'z'.

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

Add '7' to each side of the equation.
-7 + 7 + z = 2.645751311 + 7

Combine like terms: -7 + 7 = 0
0 + z = 2.645751311 + 7
z = 2.645751311 + 7

Combine like terms: 2.645751311 + 7 = 9.645751311
z = 9.645751311

Simplifying
z = 9.645751311

Subproblem 2
z + -7 = -2.645751311

Simplifying
z + -7 = -2.645751311

Reorder the terms:
-7 + z = -2.645751311

Solving
-7 + z = -2.645751311

Solving for variable 'z'.

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

Add '7' to each side of the equation.
-7 + 7 + z = -2.645751311 + 7

Combine like terms: -7 + 7 = 0
0 + z = -2.645751311 + 7
z = -2.645751311 + 7

Combine like terms: -2.645751311 + 7 = 4.354248689
z = 4.354248689

Simplifying
z = 4.354248689

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {9.645751311, 4.354248689}