y^2+11y-7=0

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Solution for y^2+11y-7=0 equation: 


Simplifying
y2 + 11y + -7 = 0

Reorder the terms:
-7 + 11y + y2 = 0

Solving
-7 + 11y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 11y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + 11y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 11y + y2 = 0 + 7
11y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
11y + y2 = 7

The y term is 11y.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11y + 30.25 + y2 = 7 + 30.25

Reorder the terms:
30.25 + 11y + y2 = 7 + 30.25

Combine like terms: 7 + 30.25 = 37.25
30.25 + 11y + y2 = 37.25

Factor a perfect square on the left side:
(y + 5.5)(y + 5.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(y + 5.5) equal to 6.103277808 and -6.103277808.


Subproblem 1
y + 5.5 = 6.103277808

Simplifying
y + 5.5 = 6.103277808

Reorder the terms:
5.5 + y = 6.103277808

Solving
5.5 + y = 6.103277808

Solving for variable 'y'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + y = 6.103277808 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + y = 6.103277808 + -5.5
y = 6.103277808 + -5.5

Combine like terms: 6.103277808 + -5.5 = 0.603277808
y = 0.603277808

Simplifying
y = 0.603277808


Subproblem 2
y + 5.5 = -6.103277808

Simplifying
y + 5.5 = -6.103277808

Reorder the terms:
5.5 + y = -6.103277808

Solving
5.5 + y = -6.103277808

Solving for variable 'y'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + y = -6.103277808 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + y = -6.103277808 + -5.5
y = -6.103277808 + -5.5

Combine like terms: -6.103277808 + -5.5 = -11.603277808
y = -11.603277808

Simplifying
y = -11.603277808


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.603277808, -11.603277808}

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