What are the solutions to the equation x^2+2sqrt(3)x-1=0 ?

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

Find the zeros of x^2+2sqrt(3)x-1=0

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

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x^{2} + 23 x - 1 = 0

x = - 3 + 2, x = - 2 - 3

Decimal Notation

x = 0.26794 \dots, x = - 3.73205 \dots

Solution steps

x^{2} + 23 x - 1 = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = - 3 + 2, x = - 2 - 3

2 r = 5 - r^{2}

2 x^{2} + 3 x - 6 = 0

r^{2} + 4 r + 3

3 x^{2} + 2 = 8 x

0 = 12 x^{2} - 160 x + 400

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