What are the solutions to the equation (y-5)^2=2y ?

The solutions to the equation (y-5)^2=2y are y=6+sqrt(11),y=6-sqrt(11)

Find the zeros of (y-5)^2=2y

The zeros of (y-5)^2=2y are y=6+sqrt(11),y=6-sqrt(11)

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(y - 5)^{2} = 2 y

y = 6 + 11, y = 6 - 11

Decimal Notation

y = 9.31662 \dots, y = 2.68337 \dots

Solution steps

(y - 5)^{2} = 2 y

Expand

(y - 5)^{2} : y^{2} - 10 y + 25

y^{2} - 10 y + 25 = 2 y

Move

2 y

to the left side

y^{2} - 12 y + 25 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 1 \cdot 25}{2 \cdot 1}

(- 12)^{2} - 4 \cdot 1 \cdot 25 = 211

y_{1, 2} = \frac{- ( - 12 ) \pm 2 11}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- ( - 12 ) + 2 11}{2 \cdot 1}, y_{2} = \frac{- ( - 12 ) - 2 11}{2 \cdot 1}

y = \frac{- ( - 12 ) + 2 11}{2 \cdot 1} : 6 + 11

y = \frac{- ( - 12 ) - 2 11}{2 \cdot 1} : 6 - 11

The solutions to the quadratic equation are:

y = 6 + 11, y = 6 - 11

- 18 \leq - 3

\frac{1}{3 x - 2} \leq 4

\frac{5 - x}{- 3} + \frac{2 x - 2}{- 5} = \frac{x - 1}{15}

- n^{2} - 9 n - 8

- 6 y - 11 = y^{2}

What are the solutions to the equation (y-5)^2=2y ?
The solutions to the equation (y-5)^2=2y are y=6+sqrt(11),y=6-sqrt(11)
Find the zeros of (y-5)^2=2y
The zeros of (y-5)^2=2y are y=6+sqrt(11),y=6-sqrt(11)