y^2+10y-731=0

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Solution for y^2+10y-731=0 equation: 


Simplifying
y2 + 10y + -731 = 0

Reorder the terms:
-731 + 10y + y2 = 0

Solving
-731 + 10y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '731' to each side of the equation.
-731 + 10y + 731 + y2 = 0 + 731

Reorder the terms:
-731 + 731 + 10y + y2 = 0 + 731

Combine like terms: -731 + 731 = 0
0 + 10y + y2 = 0 + 731
10y + y2 = 0 + 731

Combine like terms: 0 + 731 = 731
10y + y2 = 731

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 = 731 + 25

Reorder the terms:
25 + 10y + y2 = 731 + 25

Combine like terms: 731 + 25 = 756
25 + 10y + y2 = 756

Factor a perfect square on the left side:
(y + 5)(y + 5) = 756

Calculate the square root of the right side: 27.49545417

Break this problem into two subproblems by setting 
(y + 5) equal to 27.49545417 and -27.49545417.


Subproblem 1
y + 5 = 27.49545417

Simplifying
y + 5 = 27.49545417

Reorder the terms:
5 + y = 27.49545417

Solving
5 + y = 27.49545417

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 = 27.49545417 + -5

Combine like terms: 5 + -5 = 0
0 + y = 27.49545417 + -5
y = 27.49545417 + -5

Combine like terms: 27.49545417 + -5 = 22.49545417
y = 22.49545417

Simplifying
y = 22.49545417


Subproblem 2
y + 5 = -27.49545417

Simplifying
y + 5 = -27.49545417

Reorder the terms:
5 + y = -27.49545417

Solving
5 + y = -27.49545417

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 = -27.49545417 + -5

Combine like terms: 5 + -5 = 0
0 + y = -27.49545417 + -5
y = -27.49545417 + -5

Combine like terms: -27.49545417 + -5 = -32.49545417
y = -32.49545417

Simplifying
y = -32.49545417


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {22.49545417, -32.49545417}

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