What are the solutions to the equation x^2-2x-19=0 ?

The solutions to the equation x^2-2x-19=0 are x=1+2sqrt(5),x=1-2sqrt(5)

Find the zeros of x^2-2x-19=0

The zeros of x^2-2x-19=0 are x=1+2sqrt(5),x=1-2sqrt(5)

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x^{2} - 2 x - 19 = 0

x = 1 + 25, x = 1 - 25

Decimal Notation

x = 5.47213 \dots, x = - 3.47213 \dots

Solution steps

x^{2} - 2 x - 19 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( - 19 )}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot (- 19) = 45

x_{1, 2} = \frac{- ( - 2 ) \pm 4 5}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 4 5}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 4 5}{2 \cdot 1}

x = \frac{- ( - 2 ) + 4 5}{2 \cdot 1} : 1 + 25

x = \frac{- ( - 2 ) - 4 5}{2 \cdot 1} : 1 - 25

The solutions to the quadratic equation are:

x = 1 + 25, x = 1 - 25

x^{2} + x^{2} = 4

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

c, a^{2} = b^{2} + c^{2}

5 b^{2} + 12 b = 0

4 x^{2} + 36 x - 4 = 0

What are the solutions to the equation x^2-2x-19=0 ?
The solutions to the equation x^2-2x-19=0 are x=1+2sqrt(5),x=1-2sqrt(5)
Find the zeros of x^2-2x-19=0
The zeros of x^2-2x-19=0 are x=1+2sqrt(5),x=1-2sqrt(5)