Question

What is the exact solutions of x^2-5x-1=0

Answer 1

For this case we must find the solutions of the following quadratic equation:

`x ^ 2-5x-1 = 0`

We solve by means of

`x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}`

Where:

`a = 1\\b = -5\\c = -1`

Substituting:

`x = \frac {- (- 5) \pm \sqrt {(- 5) ^ 2-4 (1) (- 1)}} {2 (1)}\\x = \frac {5 \pm \sqrt {25 + 4}} {2}\\x = \frac {5\pm \sqrt {29}} {2}`

Finally, the roots are:

`x_ {1} = \frac {5+ \sqrt {29}} {2}\\x_ {2} = \frac {5- \sqrt {29}} {2}`

Answer:

`x_ {1} = \frac {5+ \sqrt {29}} {2}\\x_ {2} = \frac {5- \sqrt {29}} {2}`