y^2+y=4

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Solution for y^2+y=4 equation: 


Simplifying
y2 + y = 4

Reorder the terms:
y + y2 = 4

Solving
y + y2 = 4

Solving for variable 'y'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The y term is y.  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.
y + 0.25 + y2 = 4 + 0.25

Reorder the terms:
0.25 + y + y2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + y + y2 = 4.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
y + 0.5 = 2.061552813

Simplifying
y + 0.5 = 2.061552813

Reorder the terms:
0.5 + y = 2.061552813

Solving
0.5 + y = 2.061552813

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 = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.061552813 + -0.5
y = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
y = 1.561552813

Simplifying
y = 1.561552813


Subproblem 2
y + 0.5 = -2.061552813

Simplifying
y + 0.5 = -2.061552813

Reorder the terms:
0.5 + y = -2.061552813

Solving
0.5 + y = -2.061552813

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 = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.061552813 + -0.5
y = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
y = -2.561552813

Simplifying
y = -2.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.561552813, -2.561552813}

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