y^2+20y-10=0

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Solution for y^2+20y-10=0 equation: 


Simplifying
y2 + 20y + -10 = 0

Reorder the terms:
-10 + 20y + y2 = 0

Solving
-10 + 20y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 20y + 10 + y2 = 0 + 10

Reorder the terms:
-10 + 10 + 20y + y2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 20y + y2 = 0 + 10
20y + y2 = 0 + 10

Combine like terms: 0 + 10 = 10
20y + y2 = 10

The y term is 20y.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20y + 100 + y2 = 10 + 100

Reorder the terms:
100 + 20y + y2 = 10 + 100

Combine like terms: 10 + 100 = 110
100 + 20y + y2 = 110

Factor a perfect square on the left side:
(y + 10)(y + 10) = 110

Calculate the square root of the right side: 10.488088482

Break this problem into two subproblems by setting 
(y + 10) equal to 10.488088482 and -10.488088482.


Subproblem 1
y + 10 = 10.488088482

Simplifying
y + 10 = 10.488088482

Reorder the terms:
10 + y = 10.488088482

Solving
10 + y = 10.488088482

Solving for variable 'y'.

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

Add '-10' to each side of the equation.
10 + -10 + y = 10.488088482 + -10

Combine like terms: 10 + -10 = 0
0 + y = 10.488088482 + -10
y = 10.488088482 + -10

Combine like terms: 10.488088482 + -10 = 0.488088482
y = 0.488088482

Simplifying
y = 0.488088482


Subproblem 2
y + 10 = -10.488088482

Simplifying
y + 10 = -10.488088482

Reorder the terms:
10 + y = -10.488088482

Solving
10 + y = -10.488088482

Solving for variable 'y'.

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

Add '-10' to each side of the equation.
10 + -10 + y = -10.488088482 + -10

Combine like terms: 10 + -10 = 0
0 + y = -10.488088482 + -10
y = -10.488088482 + -10

Combine like terms: -10.488088482 + -10 = -20.488088482
y = -20.488088482

Simplifying
y = -20.488088482


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.488088482, -20.488088482}

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