y^2+10y+25=10

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Solution for y^2+10y+25=10 equation: 


Simplifying
y2 + 10y + 25 = 10

Reorder the terms:
25 + 10y + y2 = 10

Solving
25 + 10y + y2 = 10

Solving for variable 'y'.

Reorder the terms:
25 + -10 + 10y + y2 = 10 + -10

Combine like terms: 25 + -10 = 15
15 + 10y + y2 = 10 + -10

Combine like terms: 10 + -10 = 0
15 + 10y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 10y + -15 + y2 = 0 + -15

Reorder the terms:
15 + -15 + 10y + y2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 10y + y2 = 0 + -15
10y + y2 = 0 + -15

Combine like terms: 0 + -15 = -15
10y + y2 = -15

The y term is 10y.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10y + 25 + y2 = -15 + 25

Reorder the terms:
25 + 10y + y2 = -15 + 25

Combine like terms: -15 + 25 = 10
25 + 10y + y2 = 10

Factor a perfect square on the left side:
(y + 5)(y + 5) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(y + 5) equal to 3.16227766 and -3.16227766.


Subproblem 1
y + 5 = 3.16227766

Simplifying
y + 5 = 3.16227766

Reorder the terms:
5 + y = 3.16227766

Solving
5 + y = 3.16227766

Solving for variable 'y'.

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

Add '-5' to each side of the equation.
5 + -5 + y = 3.16227766 + -5

Combine like terms: 5 + -5 = 0
0 + y = 3.16227766 + -5
y = 3.16227766 + -5

Combine like terms: 3.16227766 + -5 = -1.83772234
y = -1.83772234

Simplifying
y = -1.83772234


Subproblem 2
y + 5 = -3.16227766

Simplifying
y + 5 = -3.16227766

Reorder the terms:
5 + y = -3.16227766

Solving
5 + y = -3.16227766

Solving for variable 'y'.

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

Add '-5' to each side of the equation.
5 + -5 + y = -3.16227766 + -5

Combine like terms: 5 + -5 = 0
0 + y = -3.16227766 + -5
y = -3.16227766 + -5

Combine like terms: -3.16227766 + -5 = -8.16227766
y = -8.16227766

Simplifying
y = -8.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.83772234, -8.16227766}

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