z^2-5z=25

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Solution for z^2-5z=25 equation: 


Simplifying
z2 + -5z = 25

Reorder the terms:
-5z + z2 = 25

Solving
-5z + z2 = 25

Solving for variable 'z'.

Reorder the terms:
-25 + -5z + z2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -5z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -5z + 25 + z2 = 0 + 25

Reorder the terms:
-25 + 25 + -5z + z2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -5z + z2 = 0 + 25
-5z + z2 = 0 + 25

Combine like terms: 0 + 25 = 25
-5z + z2 = 25

The z term is -5z.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5z + 6.25 + z2 = 25 + 6.25

Reorder the terms:
6.25 + -5z + z2 = 25 + 6.25

Combine like terms: 25 + 6.25 = 31.25
6.25 + -5z + z2 = 31.25

Factor a perfect square on the left side:
(z + -2.5)(z + -2.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(z + -2.5) equal to 5.590169944 and -5.590169944.


Subproblem 1
z + -2.5 = 5.590169944

Simplifying
z + -2.5 = 5.590169944

Reorder the terms:
-2.5 + z = 5.590169944

Solving
-2.5 + z = 5.590169944

Solving for variable 'z'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + z = 5.590169944 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + z = 5.590169944 + 2.5
z = 5.590169944 + 2.5

Combine like terms: 5.590169944 + 2.5 = 8.090169944
z = 8.090169944

Simplifying
z = 8.090169944


Subproblem 2
z + -2.5 = -5.590169944

Simplifying
z + -2.5 = -5.590169944

Reorder the terms:
-2.5 + z = -5.590169944

Solving
-2.5 + z = -5.590169944

Solving for variable 'z'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + z = -5.590169944 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + z = -5.590169944 + 2.5
z = -5.590169944 + 2.5

Combine like terms: -5.590169944 + 2.5 = -3.090169944
z = -3.090169944

Simplifying
z = -3.090169944


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {8.090169944, -3.090169944}

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