y^2+80y-1500=0

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Solution for y^2+80y-1500=0 equation: 


Simplifying
y2 + 80y + -1500 = 0

Reorder the terms:
-1500 + 80y + y2 = 0

Solving
-1500 + 80y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '1500' to each side of the equation.
-1500 + 80y + 1500 + y2 = 0 + 1500

Reorder the terms:
-1500 + 1500 + 80y + y2 = 0 + 1500

Combine like terms: -1500 + 1500 = 0
0 + 80y + y2 = 0 + 1500
80y + y2 = 0 + 1500

Combine like terms: 0 + 1500 = 1500
80y + y2 = 1500

The y term is 80y.  Take half its coefficient (40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
80y + 1600 + y2 = 1500 + 1600

Reorder the terms:
1600 + 80y + y2 = 1500 + 1600

Combine like terms: 1500 + 1600 = 3100
1600 + 80y + y2 = 3100

Factor a perfect square on the left side:
(y + 40)(y + 40) = 3100

Calculate the square root of the right side: 55.677643628

Break this problem into two subproblems by setting 
(y + 40) equal to 55.677643628 and -55.677643628.


Subproblem 1
y + 40 = 55.677643628

Simplifying
y + 40 = 55.677643628

Reorder the terms:
40 + y = 55.677643628

Solving
40 + y = 55.677643628

Solving for variable 'y'.

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

Add '-40' to each side of the equation.
40 + -40 + y = 55.677643628 + -40

Combine like terms: 40 + -40 = 0
0 + y = 55.677643628 + -40
y = 55.677643628 + -40

Combine like terms: 55.677643628 + -40 = 15.677643628
y = 15.677643628

Simplifying
y = 15.677643628


Subproblem 2
y + 40 = -55.677643628

Simplifying
y + 40 = -55.677643628

Reorder the terms:
40 + y = -55.677643628

Solving
40 + y = -55.677643628

Solving for variable 'y'.

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

Add '-40' to each side of the equation.
40 + -40 + y = -55.677643628 + -40

Combine like terms: 40 + -40 = 0
0 + y = -55.677643628 + -40
y = -55.677643628 + -40

Combine like terms: -55.677643628 + -40 = -95.677643628
y = -95.677643628

Simplifying
y = -95.677643628


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {15.677643628, -95.677643628}

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