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

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

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

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

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x (x - 2) = 1

x = 1 + 2, x = 1 - 2

Decimal Notation

x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

x (x - 2) = 1

Expand

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

x^{2} - 2 x = 1

Move

1

to the left side

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

Solve with the quadratic formula

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

(- 2)^{2} - 4 \cdot 1 \cdot (- 1) = 22

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 1 + 2, x = 1 - 2

\frac{0.018}{1.16 \cdot 1 0 ^{22}}

4 x (x + 1) = 7

16 v^{2} - 40 v + 25

(\frac{2}{5} m^{2}) (am - \frac{2}{7} t m^{3} - m^{4})

- 1.44

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