y^2-100y+24=0

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Solution for y^2-100y+24=0 equation:


Simplifying
y2 + -100y + 24 = 0

Reorder the terms:
24 + -100y + y2 = 0

Solving
24 + -100y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -100y + -24 + y2 = 0 + -24

Reorder the terms:
24 + -24 + -100y + y2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -100y + y2 = 0 + -24
-100y + y2 = 0 + -24

Combine like terms: 0 + -24 = -24
-100y + y2 = -24

The y term is -100y.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100y + 2500 + y2 = -24 + 2500

Reorder the terms:
2500 + -100y + y2 = -24 + 2500

Combine like terms: -24 + 2500 = 2476
2500 + -100y + y2 = 2476

Factor a perfect square on the left side:
(y + -50)(y + -50) = 2476

Calculate the square root of the right side: 49.759421218

Break this problem into two subproblems by setting 
(y + -50) equal to 49.759421218 and -49.759421218.

Subproblem 1

y + -50 = 49.759421218 Simplifying y + -50 = 49.759421218 Reorder the terms: -50 + y = 49.759421218 Solving -50 + y = 49.759421218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + y = 49.759421218 + 50 Combine like terms: -50 + 50 = 0 0 + y = 49.759421218 + 50 y = 49.759421218 + 50 Combine like terms: 49.759421218 + 50 = 99.759421218 y = 99.759421218 Simplifying y = 99.759421218

Subproblem 2

y + -50 = -49.759421218 Simplifying y + -50 = -49.759421218 Reorder the terms: -50 + y = -49.759421218 Solving -50 + y = -49.759421218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + y = -49.759421218 + 50 Combine like terms: -50 + 50 = 0 0 + y = -49.759421218 + 50 y = -49.759421218 + 50 Combine like terms: -49.759421218 + 50 = 0.240578782 y = 0.240578782 Simplifying y = 0.240578782

Solution

The solution to the problem is based on the solutions from the subproblems. y = {99.759421218, 0.240578782}

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