y^2+5y=4

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Solution for y^2+5y=4 equation: 


Simplifying
y2 + 5y = 4

Reorder the terms:
5y + y2 = 4

Solving
5y + y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + 5y + y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + 5y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5y + y2 = 0 + 4
5y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
5y + y2 = 4

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 4 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + 5y + y2 = 10.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(y + 2.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
y + 2.5 = 3.201562119

Simplifying
y + 2.5 = 3.201562119

Reorder the terms:
2.5 + y = 3.201562119

Solving
2.5 + y = 3.201562119

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 3.201562119 + -2.5
y = 3.201562119 + -2.5

Combine like terms: 3.201562119 + -2.5 = 0.701562119
y = 0.701562119

Simplifying
y = 0.701562119


Subproblem 2
y + 2.5 = -3.201562119

Simplifying
y + 2.5 = -3.201562119

Reorder the terms:
2.5 + y = -3.201562119

Solving
2.5 + y = -3.201562119

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -3.201562119 + -2.5
y = -3.201562119 + -2.5

Combine like terms: -3.201562119 + -2.5 = -5.701562119
y = -5.701562119

Simplifying
y = -5.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.701562119, -5.701562119}

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