What are the solutions to the equation x^2-2x-11=0 ?

The solutions to the equation x^2-2x-11=0 are x=1+2sqrt(3),x=1-2sqrt(3)

Find the zeros of x^2-2x-11=0

The zeros of x^2-2x-11=0 are x=1+2sqrt(3),x=1-2sqrt(3)

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x^{2} - 2 x - 11 = 0

x = 1 + 23, x = 1 - 23

Decimal Notation

x = 4.46410 \dots, x = - 2.46410 \dots

Solution steps

x^{2} - 2 x - 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( - 11 )}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot (- 11) = 43

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

Separate the solutions

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

x = \frac{- ( - 2 ) + 4 3}{2 \cdot 1} : 1 + 23

x = \frac{- ( - 2 ) - 4 3}{2 \cdot 1} : 1 - 23

The solutions to the quadratic equation are:

x = 1 + 23, x = 1 - 23

192 = - 16 t^{2} + 128

2 x^{2} + 16 x - 32

\frac{1}{- 1 + 2 i}

6 a^{2} - 23 a + 20

(\frac{1}{144})^{\frac{1}{2}}

What are the solutions to the equation x^2-2x-11=0 ?
The solutions to the equation x^2-2x-11=0 are x=1+2sqrt(3),x=1-2sqrt(3)
Find the zeros of x^2-2x-11=0
The zeros of x^2-2x-11=0 are x=1+2sqrt(3),x=1-2sqrt(3)