4y^2-8y-68=0

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Solution for 4y^2-8y-68=0 equation: 


Simplifying
4y2 + -8y + -68 = 0

Reorder the terms:
-68 + -8y + 4y2 = 0

Solving
-68 + -8y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-17 + -2y + y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-17 + -2y + y2)' equal to zero and attempt to solve:

Simplifying
-17 + -2y + y2 = 0

Solving
-17 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -2y + 17 + y2 = 0 + 17

Reorder the terms:
-17 + 17 + -2y + y2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2y + y2 = 0 + 17
-2y + y2 = 0 + 17

Combine like terms: 0 + 17 = 17
-2y + y2 = 17

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 17 + 1

Reorder the terms:
1 + -2y + y2 = 17 + 1

Combine like terms: 17 + 1 = 18
1 + -2y + y2 = 18

Factor a perfect square on the left side:
(y + -1)(y + -1) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(y + -1) equal to 4.242640687 and -4.242640687.


Subproblem 1
y + -1 = 4.242640687

Simplifying
y + -1 = 4.242640687

Reorder the terms:
-1 + y = 4.242640687

Solving
-1 + y = 4.242640687

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 4.242640687 + 1

Combine like terms: -1 + 1 = 0
0 + y = 4.242640687 + 1
y = 4.242640687 + 1

Combine like terms: 4.242640687 + 1 = 5.242640687
y = 5.242640687

Simplifying
y = 5.242640687


Subproblem 2
y + -1 = -4.242640687

Simplifying
y + -1 = -4.242640687

Reorder the terms:
-1 + y = -4.242640687

Solving
-1 + y = -4.242640687

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -4.242640687 + 1

Combine like terms: -1 + 1 = 0
0 + y = -4.242640687 + 1
y = -4.242640687 + 1

Combine like terms: -4.242640687 + 1 = -3.242640687
y = -3.242640687

Simplifying
y = -3.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.242640687, -3.242640687}
Solution
y = {5.242640687, -3.242640687}

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