41y^2-14y-5=0

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Solution for 41y^2-14y-5=0 equation: 


Simplifying
41y2 + -14y + -5 = 0

Reorder the terms:
-5 + -14y + 41y2 = 0

Solving
-5 + -14y + 41y2 = 0

Solving for variable 'y'.

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

Divide each side by '41'.
-0.1219512195 + -0.3414634146y + y2 = 0

Move the constant term to the right:

Add '0.1219512195' to each side of the equation.
-0.1219512195 + -0.3414634146y + 0.1219512195 + y2 = 0 + 0.1219512195

Reorder the terms:
-0.1219512195 + 0.1219512195 + -0.3414634146y + y2 = 0 + 0.1219512195

Combine like terms: -0.1219512195 + 0.1219512195 = 0.0000000000
0.0000000000 + -0.3414634146y + y2 = 0 + 0.1219512195
-0.3414634146y + y2 = 0 + 0.1219512195

Combine like terms: 0 + 0.1219512195 = 0.1219512195
-0.3414634146y + y2 = 0.1219512195

The y term is -0.3414634146y.  Take half its coefficient (-0.1707317073).
Square it (0.02914931588) and add it to both sides.

Add '0.02914931588' to each side of the equation.
-0.3414634146y + 0.02914931588 + y2 = 0.1219512195 + 0.02914931588

Reorder the terms:
0.02914931588 + -0.3414634146y + y2 = 0.1219512195 + 0.02914931588

Combine like terms: 0.1219512195 + 0.02914931588 = 0.15110053538
0.02914931588 + -0.3414634146y + y2 = 0.15110053538

Factor a perfect square on the left side:
(y + -0.1707317073)(y + -0.1707317073) = 0.15110053538

Calculate the square root of the right side: 0.388716523

Break this problem into two subproblems by setting 
(y + -0.1707317073) equal to 0.388716523 and -0.388716523.


Subproblem 1
y + -0.1707317073 = 0.388716523

Simplifying
y + -0.1707317073 = 0.388716523

Reorder the terms:
-0.1707317073 + y = 0.388716523

Solving
-0.1707317073 + y = 0.388716523

Solving for variable 'y'.

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

Add '0.1707317073' to each side of the equation.
-0.1707317073 + 0.1707317073 + y = 0.388716523 + 0.1707317073

Combine like terms: -0.1707317073 + 0.1707317073 = 0.0000000000
0.0000000000 + y = 0.388716523 + 0.1707317073
y = 0.388716523 + 0.1707317073

Combine like terms: 0.388716523 + 0.1707317073 = 0.5594482303
y = 0.5594482303

Simplifying
y = 0.5594482303


Subproblem 2
y + -0.1707317073 = -0.388716523

Simplifying
y + -0.1707317073 = -0.388716523

Reorder the terms:
-0.1707317073 + y = -0.388716523

Solving
-0.1707317073 + y = -0.388716523

Solving for variable 'y'.

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

Add '0.1707317073' to each side of the equation.
-0.1707317073 + 0.1707317073 + y = -0.388716523 + 0.1707317073

Combine like terms: -0.1707317073 + 0.1707317073 = 0.0000000000
0.0000000000 + y = -0.388716523 + 0.1707317073
y = -0.388716523 + 0.1707317073

Combine like terms: -0.388716523 + 0.1707317073 = -0.2179848157
y = -0.2179848157

Simplifying
y = -0.2179848157


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.5594482303, -0.2179848157}

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