10y^2+200y-400=0

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Solution for 10y^2+200y-400=0 equation: 


Simplifying
10y2 + 200y + -400 = 0

Reorder the terms:
-400 + 200y + 10y2 = 0

Solving
-400 + 200y + 10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-40 + 20y + y2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-40 + 20y + y2)' equal to zero and attempt to solve:

Simplifying
-40 + 20y + y2 = 0

Solving
-40 + 20y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 20y + 40 + y2 = 0 + 40

Reorder the terms:
-40 + 40 + 20y + y2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 20y + y2 = 0 + 40
20y + y2 = 0 + 40

Combine like terms: 0 + 40 = 40
20y + y2 = 40

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 = 40 + 100

Reorder the terms:
100 + 20y + y2 = 40 + 100

Combine like terms: 40 + 100 = 140
100 + 20y + y2 = 140

Factor a perfect square on the left side:
(y + 10)(y + 10) = 140

Calculate the square root of the right side: 11.832159566

Break this problem into two subproblems by setting 
(y + 10) equal to 11.832159566 and -11.832159566.


Subproblem 1
y + 10 = 11.832159566

Simplifying
y + 10 = 11.832159566

Reorder the terms:
10 + y = 11.832159566

Solving
10 + y = 11.832159566

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 = 11.832159566 + -10

Combine like terms: 10 + -10 = 0
0 + y = 11.832159566 + -10
y = 11.832159566 + -10

Combine like terms: 11.832159566 + -10 = 1.832159566
y = 1.832159566

Simplifying
y = 1.832159566


Subproblem 2
y + 10 = -11.832159566

Simplifying
y + 10 = -11.832159566

Reorder the terms:
10 + y = -11.832159566

Solving
10 + y = -11.832159566

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 = -11.832159566 + -10

Combine like terms: 10 + -10 = 0
0 + y = -11.832159566 + -10
y = -11.832159566 + -10

Combine like terms: -11.832159566 + -10 = -21.832159566
y = -21.832159566

Simplifying
y = -21.832159566


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.832159566, -21.832159566}
Solution
y = {1.832159566, -21.832159566}

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