0.0625y^2+5y-10=0

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Solution for 0.0625y^2+5y-10=0 equation: 


Simplifying
0.0625y2 + 5y + -10 = 0

Reorder the terms:
-10 + 5y + 0.0625y2 = 0

Solving
-10 + 5y + 0.0625y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
0.0625 the coefficient of the squared term: 

Divide each side by '0.0625'.
-160 + 80y + y2 = 0

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + 80y + 160 + y2 = 0 + 160

Reorder the terms:
-160 + 160 + 80y + y2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + 80y + y2 = 0 + 160
80y + y2 = 0 + 160

Combine like terms: 0 + 160 = 160
80y + y2 = 160

The y term is 80y.  Take half its coefficient (40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
80y + 1600 + y2 = 160 + 1600

Reorder the terms:
1600 + 80y + y2 = 160 + 1600

Combine like terms: 160 + 1600 = 1760
1600 + 80y + y2 = 1760

Factor a perfect square on the left side:
(y + 40)(y + 40) = 1760

Calculate the square root of the right side: 41.952353927

Break this problem into two subproblems by setting 
(y + 40) equal to 41.952353927 and -41.952353927.


Subproblem 1
y + 40 = 41.952353927

Simplifying
y + 40 = 41.952353927

Reorder the terms:
40 + y = 41.952353927

Solving
40 + y = 41.952353927

Solving for variable 'y'.

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

Add '-40' to each side of the equation.
40 + -40 + y = 41.952353927 + -40

Combine like terms: 40 + -40 = 0
0 + y = 41.952353927 + -40
y = 41.952353927 + -40

Combine like terms: 41.952353927 + -40 = 1.952353927
y = 1.952353927

Simplifying
y = 1.952353927


Subproblem 2
y + 40 = -41.952353927

Simplifying
y + 40 = -41.952353927

Reorder the terms:
40 + y = -41.952353927

Solving
40 + y = -41.952353927

Solving for variable 'y'.

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

Add '-40' to each side of the equation.
40 + -40 + y = -41.952353927 + -40

Combine like terms: 40 + -40 = 0
0 + y = -41.952353927 + -40
y = -41.952353927 + -40

Combine like terms: -41.952353927 + -40 = -81.952353927
y = -81.952353927

Simplifying
y = -81.952353927


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.952353927, -81.952353927}

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