10y^2+4y-64=0

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Solution for 10y^2+4y-64=0 equation: 


Simplifying
10y2 + 4y + -64 = 0

Reorder the terms:
-64 + 4y + 10y2 = 0

Solving
-64 + 4y + 10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 2y + 5y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-32 + 2y + 5y2)' equal to zero and attempt to solve:

Simplifying
-32 + 2y + 5y2 = 0

Solving
-32 + 2y + 5y2 = 0

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

Divide each side by '5'.
-6.4 + 0.4y + y2 = 0

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + 0.4y + 6.4 + y2 = 0 + 6.4

Reorder the terms:
-6.4 + 6.4 + 0.4y + y2 = 0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + 0.4y + y2 = 0 + 6.4
0.4y + y2 = 0 + 6.4

Combine like terms: 0 + 6.4 = 6.4
0.4y + y2 = 6.4

The y term is 0.4y.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4y + 0.04 + y2 = 6.4 + 0.04

Reorder the terms:
0.04 + 0.4y + y2 = 6.4 + 0.04

Combine like terms: 6.4 + 0.04 = 6.44
0.04 + 0.4y + y2 = 6.44

Factor a perfect square on the left side:
(y + 0.2)(y + 0.2) = 6.44

Calculate the square root of the right side: 2.537715508

Break this problem into two subproblems by setting 
(y + 0.2) equal to 2.537715508 and -2.537715508.


Subproblem 1
y + 0.2 = 2.537715508

Simplifying
y + 0.2 = 2.537715508

Reorder the terms:
0.2 + y = 2.537715508

Solving
0.2 + y = 2.537715508

Solving for variable 'y'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + y = 2.537715508 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + y = 2.537715508 + -0.2
y = 2.537715508 + -0.2

Combine like terms: 2.537715508 + -0.2 = 2.337715508
y = 2.337715508

Simplifying
y = 2.337715508


Subproblem 2
y + 0.2 = -2.537715508

Simplifying
y + 0.2 = -2.537715508

Reorder the terms:
0.2 + y = -2.537715508

Solving
0.2 + y = -2.537715508

Solving for variable 'y'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + y = -2.537715508 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + y = -2.537715508 + -0.2
y = -2.537715508 + -0.2

Combine like terms: -2.537715508 + -0.2 = -2.737715508
y = -2.737715508

Simplifying
y = -2.737715508


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.337715508, -2.737715508}
Solution
y = {2.337715508, -2.737715508}

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