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

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

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

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

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

x = 2 + 3, x = 2 - 3

Decimal Notation

x = 3.73205 \dots, x = 0.26794 \dots

Solution steps

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

Expand

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

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

Move

2 x

to the left side

x^{2} - 4 x + 1 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 1 \cdot 1 = 23

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 2 + 3, x = 2 - 3

2 x^{2} + 5 x - 52 = 0

(4 x - 3) (10 x + 7) = 0

4 x^{2} - 7 x = 15

2 x^{2} - 7 x^{2} + 8 x - 3 = 0

9 x^{2} = 36 x - 1

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