What are the solutions to the equation roots x^2-2x-1 ?

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

Find the zeros of roots x^2-2x-1

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

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roots

x^{2} - 2 x - 1

x = 1 + 2, x = 1 - 2

Solution steps

x^{2} - 2 x - 1

The roots are the intercepts with the x-axis

(y = 0)

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

2 x^{2} + 54 = - 24 x

(x - 4) (x - 3) + 2 = x - 1

\frac{x ^{2} - 1}{6} - \frac{x - 1}{4} = 3

2 (x - 8)^{2} - 35 = 7

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

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