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

The solutions to the equation (y-2)^2=2y+5 are y=3+sqrt(10),y=3-sqrt(10)

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

The zeros of (y-2)^2=2y+5 are y=3+sqrt(10),y=3-sqrt(10)

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

y = 3 + 10, y = 3 - 10

Decimal Notation

y = 6.16227 \dots, y = - 0.16227 \dots

Solution steps

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

Expand

(y - 2)^{2} : y^{2} - 4 y + 4

y^{2} - 4 y + 4 = 2 y + 5

Move

5

to the left side

y^{2} - 4 y - 1 = 2 y

Move

2 y

to the left side

y^{2} - 6 y - 1 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

(- 6)^{2} - 4 \cdot 1 \cdot (- 1) = 210

y_{1, 2} = \frac{- ( - 6 ) \pm 2 10}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- ( - 6 ) + 2 10}{2 \cdot 1}, y_{2} = \frac{- ( - 6 ) - 2 10}{2 \cdot 1}

y = \frac{- ( - 6 ) + 2 10}{2 \cdot 1} : 3 + 10

y = \frac{- ( - 6 ) - 2 10}{2 \cdot 1} : 3 - 10

The solutions to the quadratic equation are:

y = 3 + 10, y = 3 - 10

14 - 5 (x + 7)^{2} = 0

x, 3 x^{2} - 18 x + 24 = 0

(u - 6)^{2} = 64

(2 - x) (- 2 - x) + 3 = 0

x, 25 x^{2} + 9 y^{2} - 18 y + 216 = 0

What are the solutions to the equation (y-2)^2=2y+5 ?
The solutions to the equation (y-2)^2=2y+5 are y=3+sqrt(10),y=3-sqrt(10)
Find the zeros of (y-2)^2=2y+5
The zeros of (y-2)^2=2y+5 are y=3+sqrt(10),y=3-sqrt(10)