y^2-5y-3=0

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Solution for y^2-5y-3=0 equation: 


Simplifying
y2 + -5y + -3 = 0

Reorder the terms:
-3 + -5y + y2 = 0

Solving
-3 + -5y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -5y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + -5y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5y + y2 = 0 + 3
-5y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-5y + y2 = 3

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 = 3 + 6.25

Reorder the terms:
6.25 + -5y + y2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + -5y + y2 = 9.25

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(y + -2.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
y + -2.5 = 3.041381265

Simplifying
y + -2.5 = 3.041381265

Reorder the terms:
-2.5 + y = 3.041381265

Solving
-2.5 + y = 3.041381265

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 = 3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 3.041381265 + 2.5
y = 3.041381265 + 2.5

Combine like terms: 3.041381265 + 2.5 = 5.541381265
y = 5.541381265

Simplifying
y = 5.541381265


Subproblem 2
y + -2.5 = -3.041381265

Simplifying
y + -2.5 = -3.041381265

Reorder the terms:
-2.5 + y = -3.041381265

Solving
-2.5 + y = -3.041381265

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 = -3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -3.041381265 + 2.5
y = -3.041381265 + 2.5

Combine like terms: -3.041381265 + 2.5 = -0.541381265
y = -0.541381265

Simplifying
y = -0.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.541381265, -0.541381265}

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