5y^2-34y+40=0

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Solution for 5y^2-34y+40=0 equation: 


Simplifying
5y2 + -34y + 40 = 0

Reorder the terms:
40 + -34y + 5y2 = 0

Solving
40 + -34y + 5y2 = 0

Solving for variable 'y'.

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

Divide each side by '5'.
8 + -6.8y + y2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -6.8y + -8 + y2 = 0 + -8

Reorder the terms:
8 + -8 + -6.8y + y2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -6.8y + y2 = 0 + -8
-6.8y + y2 = 0 + -8

Combine like terms: 0 + -8 = -8
-6.8y + y2 = -8

The y term is -6.8y.  Take half its coefficient (-3.4).
Square it (11.56) and add it to both sides.

Add '11.56' to each side of the equation.
-6.8y + 11.56 + y2 = -8 + 11.56

Reorder the terms:
11.56 + -6.8y + y2 = -8 + 11.56

Combine like terms: -8 + 11.56 = 3.56
11.56 + -6.8y + y2 = 3.56

Factor a perfect square on the left side:
(y + -3.4)(y + -3.4) = 3.56

Calculate the square root of the right side: 1.886796226

Break this problem into two subproblems by setting 
(y + -3.4) equal to 1.886796226 and -1.886796226.


Subproblem 1
y + -3.4 = 1.886796226

Simplifying
y + -3.4 = 1.886796226

Reorder the terms:
-3.4 + y = 1.886796226

Solving
-3.4 + y = 1.886796226

Solving for variable 'y'.

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

Add '3.4' to each side of the equation.
-3.4 + 3.4 + y = 1.886796226 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + y = 1.886796226 + 3.4
y = 1.886796226 + 3.4

Combine like terms: 1.886796226 + 3.4 = 5.286796226
y = 5.286796226

Simplifying
y = 5.286796226


Subproblem 2
y + -3.4 = -1.886796226

Simplifying
y + -3.4 = -1.886796226

Reorder the terms:
-3.4 + y = -1.886796226

Solving
-3.4 + y = -1.886796226

Solving for variable 'y'.

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

Add '3.4' to each side of the equation.
-3.4 + 3.4 + y = -1.886796226 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + y = -1.886796226 + 3.4
y = -1.886796226 + 3.4

Combine like terms: -1.886796226 + 3.4 = 1.513203774
y = 1.513203774

Simplifying
y = 1.513203774


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.286796226, 1.513203774}

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