What are the solutions to the equation (z-6)^2=2z ?

The solutions to the equation (z-6)^2=2z are z=7+sqrt(13),z=7-sqrt(13)

Find the zeros of (z-6)^2=2z

The zeros of (z-6)^2=2z are z=7+sqrt(13),z=7-sqrt(13)

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(z - 6)^{2} = 2 z

z = 7 + 13, z = 7 - 13

Decimal Notation

z = 10.60555 \dots, z = 3.39444 \dots

Solution steps

(z - 6)^{2} = 2 z

Expand

(z - 6)^{2} : z^{2} - 12 z + 36

z^{2} - 12 z + 36 = 2 z

Move

2 z

to the left side

z^{2} - 14 z + 36 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 1 \cdot 36}{2 \cdot 1}

(- 14)^{2} - 4 \cdot 1 \cdot 36 = 213

z_{1, 2} = \frac{- ( - 14 ) \pm 2 13}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- ( - 14 ) + 2 13}{2 \cdot 1}, z_{2} = \frac{- ( - 14 ) - 2 13}{2 \cdot 1}

z = \frac{- ( - 14 ) + 2 13}{2 \cdot 1} : 7 + 13

z = \frac{- ( - 14 ) - 2 13}{2 \cdot 1} : 7 - 13

The solutions to the quadratic equation are:

z = 7 + 13, z = 7 - 13

5 x^{2} + 13 x - 46 = 0

x^{2} + b x = 0

p^{2} - 14 p + 44 = - 2

0 = x^{(2)} + 2 x - 15

x, z^{2} = x^{2} + x y^{2} z

What are the solutions to the equation (z-6)^2=2z ?
The solutions to the equation (z-6)^2=2z are z=7+sqrt(13),z=7-sqrt(13)
Find the zeros of (z-6)^2=2z
The zeros of (z-6)^2=2z are z=7+sqrt(13),z=7-sqrt(13)