y^2+10y-29=0

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Solution for y^2+10y-29=0 equation: 


Simplifying
y2 + 10y + -29 = 0

Reorder the terms:
-29 + 10y + y2 = 0

Solving
-29 + 10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 10y + 29 + y2 = 0 + 29

Reorder the terms:
-29 + 29 + 10y + y2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 10y + y2 = 0 + 29
10y + y2 = 0 + 29

Combine like terms: 0 + 29 = 29
10y + y2 = 29

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 = 29 + 25

Reorder the terms:
25 + 10y + y2 = 29 + 25

Combine like terms: 29 + 25 = 54
25 + 10y + y2 = 54

Factor a perfect square on the left side:
(y + 5)(y + 5) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(y + 5) equal to 7.348469228 and -7.348469228.


Subproblem 1
y + 5 = 7.348469228

Simplifying
y + 5 = 7.348469228

Reorder the terms:
5 + y = 7.348469228

Solving
5 + y = 7.348469228

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 = 7.348469228 + -5

Combine like terms: 5 + -5 = 0
0 + y = 7.348469228 + -5
y = 7.348469228 + -5

Combine like terms: 7.348469228 + -5 = 2.348469228
y = 2.348469228

Simplifying
y = 2.348469228


Subproblem 2
y + 5 = -7.348469228

Simplifying
y + 5 = -7.348469228

Reorder the terms:
5 + y = -7.348469228

Solving
5 + y = -7.348469228

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 = -7.348469228 + -5

Combine like terms: 5 + -5 = 0
0 + y = -7.348469228 + -5
y = -7.348469228 + -5

Combine like terms: -7.348469228 + -5 = -12.348469228
y = -12.348469228

Simplifying
y = -12.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.348469228, -12.348469228}

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