4y^2-13y-3=0

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Solution for 4y^2-13y-3=0 equation: 


Simplifying
4y2 + -13y + -3 = 0

Reorder the terms:
-3 + -13y + 4y2 = 0

Solving
-3 + -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'.
-0.75 + -3.25y + y2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -3.25y + 0.75 + y2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -3.25y + y2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -3.25y + y2 = 0 + 0.75
-3.25y + y2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-3.25y + y2 = 0.75

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 = 0.75 + 2.640625

Reorder the terms:
2.640625 + -3.25y + y2 = 0.75 + 2.640625

Combine like terms: 0.75 + 2.640625 = 3.390625
2.640625 + -3.25y + y2 = 3.390625

Factor a perfect square on the left side:
(y + -1.625)(y + -1.625) = 3.390625

Calculate the square root of the right side: 1.841364983

Break this problem into two subproblems by setting 
(y + -1.625) equal to 1.841364983 and -1.841364983.


Subproblem 1
y + -1.625 = 1.841364983

Simplifying
y + -1.625 = 1.841364983

Reorder the terms:
-1.625 + y = 1.841364983

Solving
-1.625 + y = 1.841364983

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 = 1.841364983 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + y = 1.841364983 + 1.625
y = 1.841364983 + 1.625

Combine like terms: 1.841364983 + 1.625 = 3.466364983
y = 3.466364983

Simplifying
y = 3.466364983


Subproblem 2
y + -1.625 = -1.841364983

Simplifying
y + -1.625 = -1.841364983

Reorder the terms:
-1.625 + y = -1.841364983

Solving
-1.625 + y = -1.841364983

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 = -1.841364983 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + y = -1.841364983 + 1.625
y = -1.841364983 + 1.625

Combine like terms: -1.841364983 + 1.625 = -0.216364983
y = -0.216364983

Simplifying
y = -0.216364983


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.466364983, -0.216364983}

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