What are the solutions to the equation (x-1)^2=2x-2 ?

The solutions to the equation (x-1)^2=2x-2 are x=3,x=1

Find the zeros of (x-1)^2=2x-2

The zeros of (x-1)^2=2x-2 are x=3,x=1

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(x - 1)^{2} = 2 x - 2

x = 3, x = 1

Solution steps

(x - 1)^{2} = 2 x - 2

Expand

(x - 1)^{2} : x^{2} - 2 x + 1

x^{2} - 2 x + 1 = 2 x - 2

Move

2

to the left side

x^{2} - 2 x + 3 = 2 x

Move

2 x

to the left side

x^{2} - 4 x + 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 1 \cdot 3}{2 \cdot 1}

(- 4)^{2} - 4 \cdot 1 \cdot 3 = 2

x_{1, 2} = \frac{- ( - 4 ) \pm 2}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 2}{2 \cdot 1}, x_{2} = \frac{- ( - 4 ) - 2}{2 \cdot 1}

x = \frac{- ( - 4 ) + 2}{2 \cdot 1} : 3

x = \frac{- ( - 4 ) - 2}{2 \cdot 1} : 1

The solutions to the quadratic equation are:

x = 3, x = 1

x^{2} + 4 x - 21 \leq 0

\frac{3 x}{25} = \frac{9}{50}

(- 2 \frac{1}{4})^{2}

3 - \frac{1}{2}

3 t^{2} - 9 = 0

What are the solutions to the equation (x-1)^2=2x-2 ?
The solutions to the equation (x-1)^2=2x-2 are x=3,x=1
Find the zeros of (x-1)^2=2x-2
The zeros of (x-1)^2=2x-2 are x=3,x=1