2450-140y+y^2=0

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Solution for 2450-140y+y^2=0 equation:


Simplifying
2450 + -140y + y2 = 0

Solving
2450 + -140y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-2450' to each side of the equation.
2450 + -140y + -2450 + y2 = 0 + -2450

Reorder the terms:
2450 + -2450 + -140y + y2 = 0 + -2450

Combine like terms: 2450 + -2450 = 0
0 + -140y + y2 = 0 + -2450
-140y + y2 = 0 + -2450

Combine like terms: 0 + -2450 = -2450
-140y + y2 = -2450

The y term is -140y.  Take half its coefficient (-70).
Square it (4900) and add it to both sides.

Add '4900' to each side of the equation.
-140y + 4900 + y2 = -2450 + 4900

Reorder the terms:
4900 + -140y + y2 = -2450 + 4900

Combine like terms: -2450 + 4900 = 2450
4900 + -140y + y2 = 2450

Factor a perfect square on the left side:
(y + -70)(y + -70) = 2450

Calculate the square root of the right side: 49.497474683

Break this problem into two subproblems by setting 
(y + -70) equal to 49.497474683 and -49.497474683.

Subproblem 1

y + -70 = 49.497474683 Simplifying y + -70 = 49.497474683 Reorder the terms: -70 + y = 49.497474683 Solving -70 + y = 49.497474683 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + y = 49.497474683 + 70 Combine like terms: -70 + 70 = 0 0 + y = 49.497474683 + 70 y = 49.497474683 + 70 Combine like terms: 49.497474683 + 70 = 119.497474683 y = 119.497474683 Simplifying y = 119.497474683

Subproblem 2

y + -70 = -49.497474683 Simplifying y + -70 = -49.497474683 Reorder the terms: -70 + y = -49.497474683 Solving -70 + y = -49.497474683 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + y = -49.497474683 + 70 Combine like terms: -70 + 70 = 0 0 + y = -49.497474683 + 70 y = -49.497474683 + 70 Combine like terms: -49.497474683 + 70 = 20.502525317 y = 20.502525317 Simplifying y = 20.502525317

Solution

The solution to the problem is based on the solutions from the subproblems. y = {119.497474683, 20.502525317}

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