4y^2-13y-25=0

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Solution for 4y^2-13y-25=0 equation: 


Simplifying
4y2 + -13y + -25 = 0

Reorder the terms:
-25 + -13y + 4y2 = 0

Solving
-25 + -13y + 4y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-6.25 + -3.25y + y2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -3.25y + 6.25 + y2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -3.25y + y2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -3.25y + y2 = 0 + 6.25
-3.25y + y2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-3.25y + y2 = 6.25

The y term is -3.25y.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25y + 2.640625 + y2 = 6.25 + 2.640625

Reorder the terms:
2.640625 + -3.25y + y2 = 6.25 + 2.640625

Combine like terms: 6.25 + 2.640625 = 8.890625
2.640625 + -3.25y + y2 = 8.890625

Factor a perfect square on the left side:
(y + -1.625)(y + -1.625) = 8.890625

Calculate the square root of the right side: 2.98171511

Break this problem into two subproblems by setting 
(y + -1.625) equal to 2.98171511 and -2.98171511.


Subproblem 1
y + -1.625 = 2.98171511

Simplifying
y + -1.625 = 2.98171511

Reorder the terms:
-1.625 + y = 2.98171511

Solving
-1.625 + y = 2.98171511

Solving for variable 'y'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + y = 2.98171511 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + y = 2.98171511 + 1.625
y = 2.98171511 + 1.625

Combine like terms: 2.98171511 + 1.625 = 4.60671511
y = 4.60671511

Simplifying
y = 4.60671511


Subproblem 2
y + -1.625 = -2.98171511

Simplifying
y + -1.625 = -2.98171511

Reorder the terms:
-1.625 + y = -2.98171511

Solving
-1.625 + y = -2.98171511

Solving for variable 'y'.

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

Add '1.625' to each side of the equation.
-1.625 + 1.625 + y = -2.98171511 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + y = -2.98171511 + 1.625
y = -2.98171511 + 1.625

Combine like terms: -2.98171511 + 1.625 = -1.35671511
y = -1.35671511

Simplifying
y = -1.35671511


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.60671511, -1.35671511}

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