z^2-14z+32=0

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Solution for z^2-14z+32=0 equation: 


Simplifying
z2 + -14z + 32 = 0

Reorder the terms:
32 + -14z + z2 = 0

Solving
32 + -14z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -14z + -32 + z2 = 0 + -32

Reorder the terms:
32 + -32 + -14z + z2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -14z + z2 = 0 + -32
-14z + z2 = 0 + -32

Combine like terms: 0 + -32 = -32
-14z + z2 = -32

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 = -32 + 49

Reorder the terms:
49 + -14z + z2 = -32 + 49

Combine like terms: -32 + 49 = 17
49 + -14z + z2 = 17

Factor a perfect square on the left side:
(z + -7)(z + -7) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(z + -7) equal to 4.123105626 and -4.123105626.


Subproblem 1
z + -7 = 4.123105626

Simplifying
z + -7 = 4.123105626

Reorder the terms:
-7 + z = 4.123105626

Solving
-7 + z = 4.123105626

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 = 4.123105626 + 7

Combine like terms: -7 + 7 = 0
0 + z = 4.123105626 + 7
z = 4.123105626 + 7

Combine like terms: 4.123105626 + 7 = 11.123105626
z = 11.123105626

Simplifying
z = 11.123105626


Subproblem 2
z + -7 = -4.123105626

Simplifying
z + -7 = -4.123105626

Reorder the terms:
-7 + z = -4.123105626

Solving
-7 + z = -4.123105626

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 = -4.123105626 + 7

Combine like terms: -7 + 7 = 0
0 + z = -4.123105626 + 7
z = -4.123105626 + 7

Combine like terms: -4.123105626 + 7 = 2.876894374
z = 2.876894374

Simplifying
z = 2.876894374


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {11.123105626, 2.876894374}

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