y^2+8y+16=7

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Solution for y^2+8y+16=7 equation: 


Simplifying
y2 + 8y + 16 = 7

Reorder the terms:
16 + 8y + y2 = 7

Solving
16 + 8y + y2 = 7

Solving for variable 'y'.

Reorder the terms:
16 + -7 + 8y + y2 = 7 + -7

Combine like terms: 16 + -7 = 9
9 + 8y + y2 = 7 + -7

Combine like terms: 7 + -7 = 0
9 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 8y + -9 + y2 = 0 + -9

Reorder the terms:
9 + -9 + 8y + y2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8y + y2 = 0 + -9
8y + y2 = 0 + -9

Combine like terms: 0 + -9 = -9
8y + y2 = -9

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = -9 + 16

Reorder the terms:
16 + 8y + y2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + 8y + y2 = 7

Factor a perfect square on the left side:
(y + 4)(y + 4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + 4) equal to 2.645751311 and -2.645751311.


Subproblem 1
y + 4 = 2.645751311

Simplifying
y + 4 = 2.645751311

Reorder the terms:
4 + y = 2.645751311

Solving
4 + y = 2.645751311

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = 2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + y = 2.645751311 + -4
y = 2.645751311 + -4

Combine like terms: 2.645751311 + -4 = -1.354248689
y = -1.354248689

Simplifying
y = -1.354248689


Subproblem 2
y + 4 = -2.645751311

Simplifying
y + 4 = -2.645751311

Reorder the terms:
4 + y = -2.645751311

Solving
4 + y = -2.645751311

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = -2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + y = -2.645751311 + -4
y = -2.645751311 + -4

Combine like terms: -2.645751311 + -4 = -6.645751311
y = -6.645751311

Simplifying
y = -6.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.354248689, -6.645751311}

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