y^2-34y-273=0

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Solution for y^2-34y-273=0 equation: 


Simplifying
y2 + -34y + -273 = 0

Reorder the terms:
-273 + -34y + y2 = 0

Solving
-273 + -34y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '273' to each side of the equation.
-273 + -34y + 273 + y2 = 0 + 273

Reorder the terms:
-273 + 273 + -34y + y2 = 0 + 273

Combine like terms: -273 + 273 = 0
0 + -34y + y2 = 0 + 273
-34y + y2 = 0 + 273

Combine like terms: 0 + 273 = 273
-34y + y2 = 273

The y term is -34y.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34y + 289 + y2 = 273 + 289

Reorder the terms:
289 + -34y + y2 = 273 + 289

Combine like terms: 273 + 289 = 562
289 + -34y + y2 = 562

Factor a perfect square on the left side:
(y + -17)(y + -17) = 562

Calculate the square root of the right side: 23.706539182

Break this problem into two subproblems by setting 
(y + -17) equal to 23.706539182 and -23.706539182.


Subproblem 1
y + -17 = 23.706539182

Simplifying
y + -17 = 23.706539182

Reorder the terms:
-17 + y = 23.706539182

Solving
-17 + y = 23.706539182

Solving for variable 'y'.

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

Add '17' to each side of the equation.
-17 + 17 + y = 23.706539182 + 17

Combine like terms: -17 + 17 = 0
0 + y = 23.706539182 + 17
y = 23.706539182 + 17

Combine like terms: 23.706539182 + 17 = 40.706539182
y = 40.706539182

Simplifying
y = 40.706539182


Subproblem 2
y + -17 = -23.706539182

Simplifying
y + -17 = -23.706539182

Reorder the terms:
-17 + y = -23.706539182

Solving
-17 + y = -23.706539182

Solving for variable 'y'.

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

Add '17' to each side of the equation.
-17 + 17 + y = -23.706539182 + 17

Combine like terms: -17 + 17 = 0
0 + y = -23.706539182 + 17
y = -23.706539182 + 17

Combine like terms: -23.706539182 + 17 = -6.706539182
y = -6.706539182

Simplifying
y = -6.706539182


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {40.706539182, -6.706539182}

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