y^2-10y+25=y

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Solution for y^2-10y+25=y equation:


Simplifying
y2 + -10y + 25 = y

Reorder the terms:
25 + -10y + y2 = y

Solving
25 + -10y + y2 = y

Solving for variable 'y'.

Reorder the terms:
25 + -10y + -1y + y2 = y + -1y

Combine like terms: -10y + -1y = -11y
25 + -11y + y2 = y + -1y

Combine like terms: y + -1y = 0
25 + -11y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -11y + -25 + y2 = 0 + -25

Reorder the terms:
25 + -25 + -11y + y2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -11y + y2 = 0 + -25
-11y + y2 = 0 + -25

Combine like terms: 0 + -25 = -25
-11y + y2 = -25

The y term is -11y.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11y + 30.25 + y2 = -25 + 30.25

Reorder the terms:
30.25 + -11y + y2 = -25 + 30.25

Combine like terms: -25 + 30.25 = 5.25
30.25 + -11y + y2 = 5.25

Factor a perfect square on the left side:
(y + -5.5)(y + -5.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(y + -5.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

y + -5.5 = 2.291287847 Simplifying y + -5.5 = 2.291287847 Reorder the terms: -5.5 + y = 2.291287847 Solving -5.5 + y = 2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 2.291287847 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 2.291287847 + 5.5 y = 2.291287847 + 5.5 Combine like terms: 2.291287847 + 5.5 = 7.791287847 y = 7.791287847 Simplifying y = 7.791287847

Subproblem 2

y + -5.5 = -2.291287847 Simplifying y + -5.5 = -2.291287847 Reorder the terms: -5.5 + y = -2.291287847 Solving -5.5 + y = -2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -2.291287847 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -2.291287847 + 5.5 y = -2.291287847 + 5.5 Combine like terms: -2.291287847 + 5.5 = 3.208712153 y = 3.208712153 Simplifying y = 3.208712153

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.791287847, 3.208712153}

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