y^2-46y+100=0

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Solution for y^2-46y+100=0 equation:


Simplifying
y2 + -46y + 100 = 0

Reorder the terms:
100 + -46y + y2 = 0

Solving
100 + -46y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -46y + -100 + y2 = 0 + -100

Reorder the terms:
100 + -100 + -46y + y2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -46y + y2 = 0 + -100
-46y + y2 = 0 + -100

Combine like terms: 0 + -100 = -100
-46y + y2 = -100

The y term is -46y.  Take half its coefficient (-23).
Square it (529) and add it to both sides.

Add '529' to each side of the equation.
-46y + 529 + y2 = -100 + 529

Reorder the terms:
529 + -46y + y2 = -100 + 529

Combine like terms: -100 + 529 = 429
529 + -46y + y2 = 429

Factor a perfect square on the left side:
(y + -23)(y + -23) = 429

Calculate the square root of the right side: 20.712315177

Break this problem into two subproblems by setting 
(y + -23) equal to 20.712315177 and -20.712315177.

Subproblem 1

y + -23 = 20.712315177 Simplifying y + -23 = 20.712315177 Reorder the terms: -23 + y = 20.712315177 Solving -23 + y = 20.712315177 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + y = 20.712315177 + 23 Combine like terms: -23 + 23 = 0 0 + y = 20.712315177 + 23 y = 20.712315177 + 23 Combine like terms: 20.712315177 + 23 = 43.712315177 y = 43.712315177 Simplifying y = 43.712315177

Subproblem 2

y + -23 = -20.712315177 Simplifying y + -23 = -20.712315177 Reorder the terms: -23 + y = -20.712315177 Solving -23 + y = -20.712315177 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + y = -20.712315177 + 23 Combine like terms: -23 + 23 = 0 0 + y = -20.712315177 + 23 y = -20.712315177 + 23 Combine like terms: -20.712315177 + 23 = 2.287684823 y = 2.287684823 Simplifying y = 2.287684823

Solution

The solution to the problem is based on the solutions from the subproblems. y = {43.712315177, 2.287684823}

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