y^2-100=4y

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Solution for y^2-100=4y equation:


Simplifying
y2 + -100 = 4y

Reorder the terms:
-100 + y2 = 4y

Solving
-100 + y2 = 4y

Solving for variable 'y'.

Reorder the terms:
-100 + -4y + y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-100 + -4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -4y + 100 + y2 = 0 + 100

Reorder the terms:
-100 + 100 + -4y + y2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -4y + y2 = 0 + 100
-4y + y2 = 0 + 100

Combine like terms: 0 + 100 = 100
-4y + y2 = 100

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 = 100 + 4

Reorder the terms:
4 + -4y + y2 = 100 + 4

Combine like terms: 100 + 4 = 104
4 + -4y + y2 = 104

Factor a perfect square on the left side:
(y + -2)(y + -2) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(y + -2) equal to 10.198039027 and -10.198039027.

Subproblem 1

y + -2 = 10.198039027 Simplifying y + -2 = 10.198039027 Reorder the terms: -2 + y = 10.198039027 Solving -2 + y = 10.198039027 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 = 10.198039027 + 2 Combine like terms: -2 + 2 = 0 0 + y = 10.198039027 + 2 y = 10.198039027 + 2 Combine like terms: 10.198039027 + 2 = 12.198039027 y = 12.198039027 Simplifying y = 12.198039027

Subproblem 2

y + -2 = -10.198039027 Simplifying y + -2 = -10.198039027 Reorder the terms: -2 + y = -10.198039027 Solving -2 + y = -10.198039027 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 = -10.198039027 + 2 Combine like terms: -2 + 2 = 0 0 + y = -10.198039027 + 2 y = -10.198039027 + 2 Combine like terms: -10.198039027 + 2 = -8.198039027 y = -8.198039027 Simplifying y = -8.198039027

Solution

The solution to the problem is based on the solutions from the subproblems. y = {12.198039027, -8.198039027}

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