y^2-4y-47=0

Solution for y^2-4y-47=0 equation:

Simplifying
y2 + -4y + -47 = 0

Reorder the terms:
-47 + -4y + y2 = 0

Solving
-47 + -4y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -4y + 47 + y2 = 0 + 47

Reorder the terms:
-47 + 47 + -4y + y2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -4y + y2 = 0 + 47
-4y + y2 = 0 + 47

Combine like terms: 0 + 47 = 47
-4y + y2 = 47

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 47 + 4

Reorder the terms:
4 + -4y + y2 = 47 + 4

Combine like terms: 47 + 4 = 51
4 + -4y + y2 = 51

Factor a perfect square on the left side:
(y + -2)(y + -2) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(y + -2) equal to 7.141428429 and -7.141428429.

Subproblem 1
y + -2 = 7.141428429

Simplifying
y + -2 = 7.141428429

Reorder the terms:
-2 + y = 7.141428429

Solving
-2 + y = 7.141428429

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 7.141428429 + 2

Combine like terms: -2 + 2 = 0
0 + y = 7.141428429 + 2
y = 7.141428429 + 2

Combine like terms: 7.141428429 + 2 = 9.141428429
y = 9.141428429

Simplifying
y = 9.141428429

Subproblem 2
y + -2 = -7.141428429

Simplifying
y + -2 = -7.141428429

Reorder the terms:
-2 + y = -7.141428429

Solving
-2 + y = -7.141428429

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -7.141428429 + 2

Combine like terms: -2 + 2 = 0
0 + y = -7.141428429 + 2
y = -7.141428429 + 2

Combine like terms: -7.141428429 + 2 = -5.141428429
y = -5.141428429

Simplifying
y = -5.141428429

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.141428429, -5.141428429}