5y^2-40y+50=0

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Solution for 5y^2-40y+50=0 equation: 


Simplifying
5y2 + -40y + 50 = 0

Reorder the terms:
50 + -40y + 5y2 = 0

Solving
50 + -40y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(10 + -8y + y2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(10 + -8y + y2)' equal to zero and attempt to solve:

Simplifying
10 + -8y + y2 = 0

Solving
10 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -8y + -10 + y2 = 0 + -10

Reorder the terms:
10 + -10 + -8y + y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -8y + y2 = 0 + -10
-8y + y2 = 0 + -10

Combine like terms: 0 + -10 = -10
-8y + y2 = -10

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = -10 + 16

Reorder the terms:
16 + -8y + y2 = -10 + 16

Combine like terms: -10 + 16 = 6
16 + -8y + y2 = 6

Factor a perfect square on the left side:
(y + -4)(y + -4) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(y + -4) equal to 2.449489743 and -2.449489743.


Subproblem 1
y + -4 = 2.449489743

Simplifying
y + -4 = 2.449489743

Reorder the terms:
-4 + y = 2.449489743

Solving
-4 + y = 2.449489743

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 2.449489743 + 4

Combine like terms: -4 + 4 = 0
0 + y = 2.449489743 + 4
y = 2.449489743 + 4

Combine like terms: 2.449489743 + 4 = 6.449489743
y = 6.449489743

Simplifying
y = 6.449489743


Subproblem 2
y + -4 = -2.449489743

Simplifying
y + -4 = -2.449489743

Reorder the terms:
-4 + y = -2.449489743

Solving
-4 + y = -2.449489743

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -2.449489743 + 4

Combine like terms: -4 + 4 = 0
0 + y = -2.449489743 + 4
y = -2.449489743 + 4

Combine like terms: -2.449489743 + 4 = 1.550510257
y = 1.550510257

Simplifying
y = 1.550510257


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.449489743, 1.550510257}
Solution
y = {6.449489743, 1.550510257}

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