10y^2-10y-280=0

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Solution for 10y^2-10y-280=0 equation: 


Simplifying
10y2 + -10y + -280 = 0

Reorder the terms:
-280 + -10y + 10y2 = 0

Solving
-280 + -10y + 10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-28 + -1y + y2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-28 + -1y + y2)' equal to zero and attempt to solve:

Simplifying
-28 + -1y + y2 = 0

Solving
-28 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -1y + 28 + y2 = 0 + 28

Reorder the terms:
-28 + 28 + -1y + y2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -1y + y2 = 0 + 28
-1y + y2 = 0 + 28

Combine like terms: 0 + 28 = 28
-1y + y2 = 28

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 28 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 28 + 0.25

Combine like terms: 28 + 0.25 = 28.25
0.25 + -1y + y2 = 28.25

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(y + -0.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
y + -0.5 = 5.315072906

Simplifying
y + -0.5 = 5.315072906

Reorder the terms:
-0.5 + y = 5.315072906

Solving
-0.5 + y = 5.315072906

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 5.315072906 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 5.315072906 + 0.5
y = 5.315072906 + 0.5

Combine like terms: 5.315072906 + 0.5 = 5.815072906
y = 5.815072906

Simplifying
y = 5.815072906


Subproblem 2
y + -0.5 = -5.315072906

Simplifying
y + -0.5 = -5.315072906

Reorder the terms:
-0.5 + y = -5.315072906

Solving
-0.5 + y = -5.315072906

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -5.315072906 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -5.315072906 + 0.5
y = -5.315072906 + 0.5

Combine like terms: -5.315072906 + 0.5 = -4.815072906
y = -4.815072906

Simplifying
y = -4.815072906


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.815072906, -4.815072906}
Solution
y = {5.815072906, -4.815072906}

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