y^2-10y+25-48=0

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Solution for y^2-10y+25-48=0 equation: 


Simplifying
y2 + -10y + 25 + -48 = 0

Reorder the terms:
25 + -48 + -10y + y2 = 0

Combine like terms: 25 + -48 = -23
-23 + -10y + y2 = 0

Solving
-23 + -10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -10y + 23 + y2 = 0 + 23

Reorder the terms:
-23 + 23 + -10y + y2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -10y + y2 = 0 + 23
-10y + y2 = 0 + 23

Combine like terms: 0 + 23 = 23
-10y + y2 = 23

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = 23 + 25

Reorder the terms:
25 + -10y + y2 = 23 + 25

Combine like terms: 23 + 25 = 48
25 + -10y + y2 = 48

Factor a perfect square on the left side:
(y + -5)(y + -5) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(y + -5) equal to 6.92820323 and -6.92820323.


Subproblem 1
y + -5 = 6.92820323

Simplifying
y + -5 = 6.92820323

Reorder the terms:
-5 + y = 6.92820323

Solving
-5 + y = 6.92820323

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = 6.92820323 + 5

Combine like terms: -5 + 5 = 0
0 + y = 6.92820323 + 5
y = 6.92820323 + 5

Combine like terms: 6.92820323 + 5 = 11.92820323
y = 11.92820323

Simplifying
y = 11.92820323


Subproblem 2
y + -5 = -6.92820323

Simplifying
y + -5 = -6.92820323

Reorder the terms:
-5 + y = -6.92820323

Solving
-5 + y = -6.92820323

Solving for variable 'y'.

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

Add '5' to each side of the equation.
-5 + 5 + y = -6.92820323 + 5

Combine like terms: -5 + 5 = 0
0 + y = -6.92820323 + 5
y = -6.92820323 + 5

Combine like terms: -6.92820323 + 5 = -1.92820323
y = -1.92820323

Simplifying
y = -1.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.92820323, -1.92820323}

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