Question

Please help with 1 Math question!!!

Solve.

x2−5x−8=0

Enter your answers, as exact values, in the boxes

x = ___ and x = ____

Answer 1

For this case we must solve the following quadratic equation:

`x ^ 2-5x-8 = 0`

We use the quadratic formula to find the solutions:

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

Where:

`a = 1\\b = -5\\c = -8`

Substituting we have:

`x = \frac {- (- 5) \pm \sqrt {(- 5) ^ 2-4 (1) (- 8)}} {2 (1)}\\x = \frac {5 \pm \sqrt {25 + 32}} {2}\\x = \frac {5 \pm \sqrt {57}} {2}`

In this way we have two roots:

`x_ {1} = \frac {5+ \sqrt {57}} {2}\\x_ {2} = \frac {5- \sqrt {57}} {2}`

Answer:

`x_ {1} = \frac {5+ \sqrt {57}} {2}\\x_ {2} = \frac {5- \sqrt {57}} {2}`