y^2=y+8.75

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Solution for y^2=y+8.75 equation: 


Simplifying
y2 = y + 8.75

Reorder the terms:
y2 = 8.75 + y

Solving
y2 = 8.75 + y

Solving for variable 'y'.

Reorder the terms:
-8.75 + -1y + y2 = 8.75 + y + -8.75 + -1y

Reorder the terms:
-8.75 + -1y + y2 = 8.75 + -8.75 + y + -1y

Combine like terms: 8.75 + -8.75 = 0.00
-8.75 + -1y + y2 = 0.00 + y + -1y
-8.75 + -1y + y2 = y + -1y

Combine like terms: y + -1y = 0
-8.75 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + -1y + 8.75 + y2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + -1y + y2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + -1y + y2 = 0 + 8.75
-1y + y2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
-1y + y2 = 8.75

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 8.75 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 8.75 + 0.25

Combine like terms: 8.75 + 0.25 = 9
0.25 + -1y + y2 = 9

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(y + -0.5) equal to 3 and -3.


Subproblem 1
y + -0.5 = 3

Simplifying
y + -0.5 = 3

Reorder the terms:
-0.5 + y = 3

Solving
-0.5 + y = 3

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 3 + 0.5
y = 3 + 0.5

Combine like terms: 3 + 0.5 = 3.5
y = 3.5

Simplifying
y = 3.5


Subproblem 2
y + -0.5 = -3

Simplifying
y + -0.5 = -3

Reorder the terms:
-0.5 + y = -3

Solving
-0.5 + y = -3

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -3 + 0.5
y = -3 + 0.5

Combine like terms: -3 + 0.5 = -2.5
y = -2.5

Simplifying
y = -2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.5, -2.5}

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