y^2-240y+11000=0

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Solution for y^2-240y+11000=0 equation:


Simplifying
y2 + -240y + 11000 = 0

Reorder the terms:
11000 + -240y + y2 = 0

Solving
11000 + -240y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-11000' to each side of the equation.
11000 + -240y + -11000 + y2 = 0 + -11000

Reorder the terms:
11000 + -11000 + -240y + y2 = 0 + -11000

Combine like terms: 11000 + -11000 = 0
0 + -240y + y2 = 0 + -11000
-240y + y2 = 0 + -11000

Combine like terms: 0 + -11000 = -11000
-240y + y2 = -11000

The y term is -240y.  Take half its coefficient (-120).
Square it (14400) and add it to both sides.

Add '14400' to each side of the equation.
-240y + 14400 + y2 = -11000 + 14400

Reorder the terms:
14400 + -240y + y2 = -11000 + 14400

Combine like terms: -11000 + 14400 = 3400
14400 + -240y + y2 = 3400

Factor a perfect square on the left side:
(y + -120)(y + -120) = 3400

Calculate the square root of the right side: 58.309518948

Break this problem into two subproblems by setting 
(y + -120) equal to 58.309518948 and -58.309518948.

Subproblem 1

y + -120 = 58.309518948 Simplifying y + -120 = 58.309518948 Reorder the terms: -120 + y = 58.309518948 Solving -120 + y = 58.309518948 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + y = 58.309518948 + 120 Combine like terms: -120 + 120 = 0 0 + y = 58.309518948 + 120 y = 58.309518948 + 120 Combine like terms: 58.309518948 + 120 = 178.309518948 y = 178.309518948 Simplifying y = 178.309518948

Subproblem 2

y + -120 = -58.309518948 Simplifying y + -120 = -58.309518948 Reorder the terms: -120 + y = -58.309518948 Solving -120 + y = -58.309518948 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + y = -58.309518948 + 120 Combine like terms: -120 + 120 = 0 0 + y = -58.309518948 + 120 y = -58.309518948 + 120 Combine like terms: -58.309518948 + 120 = 61.690481052 y = 61.690481052 Simplifying y = 61.690481052

Solution

The solution to the problem is based on the solutions from the subproblems. y = {178.309518948, 61.690481052}

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