y^2-7y-34=0

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Solution for y^2-7y-34=0 equation: 


Simplifying
y2 + -7y + -34 = 0

Reorder the terms:
-34 + -7y + y2 = 0

Solving
-34 + -7y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -7y + 34 + y2 = 0 + 34

Reorder the terms:
-34 + 34 + -7y + y2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -7y + y2 = 0 + 34
-7y + y2 = 0 + 34

Combine like terms: 0 + 34 = 34
-7y + y2 = 34

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = 34 + 12.25

Reorder the terms:
12.25 + -7y + y2 = 34 + 12.25

Combine like terms: 34 + 12.25 = 46.25
12.25 + -7y + y2 = 46.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(y + -3.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
y + -3.5 = 6.800735254

Simplifying
y + -3.5 = 6.800735254

Reorder the terms:
-3.5 + y = 6.800735254

Solving
-3.5 + y = 6.800735254

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = 6.800735254 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 6.800735254 + 3.5
y = 6.800735254 + 3.5

Combine like terms: 6.800735254 + 3.5 = 10.300735254
y = 10.300735254

Simplifying
y = 10.300735254


Subproblem 2
y + -3.5 = -6.800735254

Simplifying
y + -3.5 = -6.800735254

Reorder the terms:
-3.5 + y = -6.800735254

Solving
-3.5 + y = -6.800735254

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = -6.800735254 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -6.800735254 + 3.5
y = -6.800735254 + 3.5

Combine like terms: -6.800735254 + 3.5 = -3.300735254
y = -3.300735254

Simplifying
y = -3.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.300735254, -3.300735254}

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