(z^2)-14z+13=323

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Solution for (z^2)-14z+13=323 equation: 


Simplifying
(z2) + -14z + 13 = 323
z2 + -14z + 13 = 323

Reorder the terms:
13 + -14z + z2 = 323

Solving
13 + -14z + z2 = 323

Solving for variable 'z'.

Reorder the terms:
13 + -323 + -14z + z2 = 323 + -323

Combine like terms: 13 + -323 = -310
-310 + -14z + z2 = 323 + -323

Combine like terms: 323 + -323 = 0
-310 + -14z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '310' to each side of the equation.
-310 + -14z + 310 + z2 = 0 + 310

Reorder the terms:
-310 + 310 + -14z + z2 = 0 + 310

Combine like terms: -310 + 310 = 0
0 + -14z + z2 = 0 + 310
-14z + z2 = 0 + 310

Combine like terms: 0 + 310 = 310
-14z + z2 = 310

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 = 310 + 49

Reorder the terms:
49 + -14z + z2 = 310 + 49

Combine like terms: 310 + 49 = 359
49 + -14z + z2 = 359

Factor a perfect square on the left side:
(z + -7)(z + -7) = 359

Calculate the square root of the right side: 18.947295321

Break this problem into two subproblems by setting 
(z + -7) equal to 18.947295321 and -18.947295321.


Subproblem 1
z + -7 = 18.947295321

Simplifying
z + -7 = 18.947295321

Reorder the terms:
-7 + z = 18.947295321

Solving
-7 + z = 18.947295321

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 = 18.947295321 + 7

Combine like terms: -7 + 7 = 0
0 + z = 18.947295321 + 7
z = 18.947295321 + 7

Combine like terms: 18.947295321 + 7 = 25.947295321
z = 25.947295321

Simplifying
z = 25.947295321


Subproblem 2
z + -7 = -18.947295321

Simplifying
z + -7 = -18.947295321

Reorder the terms:
-7 + z = -18.947295321

Solving
-7 + z = -18.947295321

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 = -18.947295321 + 7

Combine like terms: -7 + 7 = 0
0 + z = -18.947295321 + 7
z = -18.947295321 + 7

Combine like terms: -18.947295321 + 7 = -11.947295321
z = -11.947295321

Simplifying
z = -11.947295321


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {25.947295321, -11.947295321}

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