8y^2+37y-5=

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Solution for 8y^2+37y-5= equation: 


Simplifying
8y2 + 37y + -5 = 0

Reorder the terms:
-5 + 37y + 8y2 = 0

Solving
-5 + 37y + 8y2 = 0

Solving for variable 'y'.

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

Divide each side by '8'.
-0.625 + 4.625y + y2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 4.625y + 0.625 + y2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 4.625y + y2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 4.625y + y2 = 0 + 0.625
4.625y + y2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
4.625y + y2 = 0.625

The y term is 4.625y.  Take half its coefficient (2.3125).
Square it (5.34765625) and add it to both sides.

Add '5.34765625' to each side of the equation.
4.625y + 5.34765625 + y2 = 0.625 + 5.34765625

Reorder the terms:
5.34765625 + 4.625y + y2 = 0.625 + 5.34765625

Combine like terms: 0.625 + 5.34765625 = 5.97265625
5.34765625 + 4.625y + y2 = 5.97265625

Factor a perfect square on the left side:
(y + 2.3125)(y + 2.3125) = 5.97265625

Calculate the square root of the right side: 2.44390185

Break this problem into two subproblems by setting 
(y + 2.3125) equal to 2.44390185 and -2.44390185.


Subproblem 1
y + 2.3125 = 2.44390185

Simplifying
y + 2.3125 = 2.44390185

Reorder the terms:
2.3125 + y = 2.44390185

Solving
2.3125 + y = 2.44390185

Solving for variable 'y'.

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

Add '-2.3125' to each side of the equation.
2.3125 + -2.3125 + y = 2.44390185 + -2.3125

Combine like terms: 2.3125 + -2.3125 = 0.0000
0.0000 + y = 2.44390185 + -2.3125
y = 2.44390185 + -2.3125

Combine like terms: 2.44390185 + -2.3125 = 0.13140185
y = 0.13140185

Simplifying
y = 0.13140185


Subproblem 2
y + 2.3125 = -2.44390185

Simplifying
y + 2.3125 = -2.44390185

Reorder the terms:
2.3125 + y = -2.44390185

Solving
2.3125 + y = -2.44390185

Solving for variable 'y'.

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

Add '-2.3125' to each side of the equation.
2.3125 + -2.3125 + y = -2.44390185 + -2.3125

Combine like terms: 2.3125 + -2.3125 = 0.0000
0.0000 + y = -2.44390185 + -2.3125
y = -2.44390185 + -2.3125

Combine like terms: -2.44390185 + -2.3125 = -4.75640185
y = -4.75640185

Simplifying
y = -4.75640185


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.13140185, -4.75640185}

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