What are the solutions to the equation (y-2)^2-10(y-2)=-9 ?

The solutions to the equation (y-2)^2-10(y-2)=-9 are y=11,y=3

Find the zeros of (y-2)^2-10(y-2)=-9

The zeros of (y-2)^2-10(y-2)=-9 are y=11,y=3

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(y - 2)^{2} - 10 (y - 2) = - 9

y = 11, y = 3

Solution steps

(y - 2)^{2} - 10 (y - 2) = - 9

Expand

(y - 2)^{2} - 10 (y - 2) : y^{2} - 14 y + 24

y^{2} - 14 y + 24 = - 9

Move

9

to the left side

y^{2} - 14 y + 33 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 1 \cdot 33}{2 \cdot 1}

(- 14)^{2} - 4 \cdot 1 \cdot 33 = 8

y_{1, 2} = \frac{- ( - 14 ) \pm 8}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- ( - 14 ) + 8}{2 \cdot 1}, y_{2} = \frac{- ( - 14 ) - 8}{2 \cdot 1}

y = \frac{- ( - 14 ) + 8}{2 \cdot 1} : 11

y = \frac{- ( - 14 ) - 8}{2 \cdot 1} : 3

The solutions to the quadratic equation are:

y = 11, y = 3

5 n (n - 4) = 0

12 x^{2} + 23 x + 10 = 0

x^{2} + x - 32 = 0

(2 x - 1) (x + 3) = 4

2 y^{2} + 7 y - 4 = 0

What are the solutions to the equation (y-2)^2-10(y-2)=-9 ?
The solutions to the equation (y-2)^2-10(y-2)=-9 are y=11,y=3
Find the zeros of (y-2)^2-10(y-2)=-9
The zeros of (y-2)^2-10(y-2)=-9 are y=11,y=3