y^2-4y-67=0

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Solution for y^2-4y-67=0 equation: 


Simplifying
y2 + -4y + -67 = 0

Reorder the terms:
-67 + -4y + y2 = 0

Solving
-67 + -4y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '67' to each side of the equation.
-67 + -4y + 67 + y2 = 0 + 67

Reorder the terms:
-67 + 67 + -4y + y2 = 0 + 67

Combine like terms: -67 + 67 = 0
0 + -4y + y2 = 0 + 67
-4y + y2 = 0 + 67

Combine like terms: 0 + 67 = 67
-4y + y2 = 67

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 67 + 4

Reorder the terms:
4 + -4y + y2 = 67 + 4

Combine like terms: 67 + 4 = 71
4 + -4y + y2 = 71

Factor a perfect square on the left side:
(y + -2)(y + -2) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(y + -2) equal to 8.426149773 and -8.426149773.


Subproblem 1
y + -2 = 8.426149773

Simplifying
y + -2 = 8.426149773

Reorder the terms:
-2 + y = 8.426149773

Solving
-2 + y = 8.426149773

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 8.426149773 + 2

Combine like terms: -2 + 2 = 0
0 + y = 8.426149773 + 2
y = 8.426149773 + 2

Combine like terms: 8.426149773 + 2 = 10.426149773
y = 10.426149773

Simplifying
y = 10.426149773


Subproblem 2
y + -2 = -8.426149773

Simplifying
y + -2 = -8.426149773

Reorder the terms:
-2 + y = -8.426149773

Solving
-2 + y = -8.426149773

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -8.426149773 + 2

Combine like terms: -2 + 2 = 0
0 + y = -8.426149773 + 2
y = -8.426149773 + 2

Combine like terms: -8.426149773 + 2 = -6.426149773
y = -6.426149773

Simplifying
y = -6.426149773


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.426149773, -6.426149773}

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