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

The solutions to the equation (x-2)^2=2x-1 are x=5,x=1

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

The zeros of (x-2)^2=2x-1 are x=5,x=1

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

x = 5, x = 1

Solution steps

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

Expand

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

x^{2} - 4 x + 4 = 2 x - 1

Move

1

to the left side

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

Move

2 x

to the left side

x^{2} - 6 x + 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 1 \cdot 5}{2 \cdot 1}

(- 6)^{2} - 4 \cdot 1 \cdot 5 = 4

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

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 4}{2 \cdot 1}, x_{2} = \frac{- ( - 6 ) - 4}{2 \cdot 1}

x = \frac{- ( - 6 ) + 4}{2 \cdot 1} : 5

x = \frac{- ( - 6 ) - 4}{2 \cdot 1} : 1

The solutions to the quadratic equation are:

x = 5, x = 1

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

t, t = \frac{2 a ( b t ^{2} + n )}{3} + \frac{d}{2}

(x - 1)^{2} - 16 = 1

6 n^{2} = - 12 n - 1

x, x^{2} y + x y = 1

What are the solutions to the equation (x-2)^2=2x-1 ?
The solutions to the equation (x-2)^2=2x-1 are x=5,x=1
Find the zeros of (x-2)^2=2x-1
The zeros of (x-2)^2=2x-1 are x=5,x=1