y^2-11=-4y

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Solution for y^2-11=-4y equation:


Simplifying
y2 + -11 = -4y

Reorder the terms:
-11 + y2 = -4y

Solving
-11 + y2 = -4y

Solving for variable 'y'.

Reorder the terms:
-11 + 4y + y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
-11 + 4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 4y + 11 + y2 = 0 + 11

Reorder the terms:
-11 + 11 + 4y + y2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 4y + y2 = 0 + 11
4y + y2 = 0 + 11

Combine like terms: 0 + 11 = 11
4y + y2 = 11

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 = 11 + 4

Reorder the terms:
4 + 4y + y2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + 4y + y2 = 15

Factor a perfect square on the left side:
(y + 2)(y + 2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(y + 2) equal to 3.872983346 and -3.872983346.

Subproblem 1

y + 2 = 3.872983346 Simplifying y + 2 = 3.872983346 Reorder the terms: 2 + y = 3.872983346 Solving 2 + y = 3.872983346 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 = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + y = 3.872983346 + -2 y = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 y = 1.872983346 Simplifying y = 1.872983346

Subproblem 2

y + 2 = -3.872983346 Simplifying y + 2 = -3.872983346 Reorder the terms: 2 + y = -3.872983346 Solving 2 + y = -3.872983346 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 = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + y = -3.872983346 + -2 y = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 y = -5.872983346 Simplifying y = -5.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.872983346, -5.872983346}

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