y^2-7y-20=0

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Solution for y^2-7y-20=0 equation: 


Simplifying
y2 + -7y + -20 = 0

Reorder the terms:
-20 + -7y + y2 = 0

Solving
-20 + -7y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -7y + 20 + y2 = 0 + 20

Reorder the terms:
-20 + 20 + -7y + y2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -7y + y2 = 0 + 20
-7y + y2 = 0 + 20

Combine like terms: 0 + 20 = 20
-7y + y2 = 20

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 = 20 + 12.25

Reorder the terms:
12.25 + -7y + y2 = 20 + 12.25

Combine like terms: 20 + 12.25 = 32.25
12.25 + -7y + y2 = 32.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(y + -3.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
y + -3.5 = 5.678908346

Simplifying
y + -3.5 = 5.678908346

Reorder the terms:
-3.5 + y = 5.678908346

Solving
-3.5 + y = 5.678908346

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 = 5.678908346 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 5.678908346 + 3.5
y = 5.678908346 + 3.5

Combine like terms: 5.678908346 + 3.5 = 9.178908346
y = 9.178908346

Simplifying
y = 9.178908346


Subproblem 2
y + -3.5 = -5.678908346

Simplifying
y + -3.5 = -5.678908346

Reorder the terms:
-3.5 + y = -5.678908346

Solving
-3.5 + y = -5.678908346

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 = -5.678908346 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -5.678908346 + 3.5
y = -5.678908346 + 3.5

Combine like terms: -5.678908346 + 3.5 = -2.178908346
y = -2.178908346

Simplifying
y = -2.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.178908346, -2.178908346}

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