y^2+1=2y

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Solution for y^2+1=2y equation:


Simplifying
y2 + 1 = 2y

Reorder the terms:
1 + y2 = 2y

Solving
1 + y2 = 2y

Solving for variable 'y'.

Reorder the terms:
1 + -2y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
1 + -2y + y2 = 0

Factor a trinomial.
(1 + -1y)(1 + -1y) = 0

Subproblem 1

Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1

Subproblem 2

Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1

Solution

y = {1, 1}

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