For this case we must factor the following expression:
[tex]x ^ 2-7x-10[/tex]
To factor, we must find two numbers that when added together give -7 and when multiplied by -10.
It is observed that there are not two whole numbers that comply with the aforementioned.
Thus, the following equation applies:
[tex]x = \frac {-b \pm\sqrt{b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 1\\b = -7\\c = -10[/tex]
We replace:
[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (1) (- 10)}} {2 (1)}\\x = \frac {7 \pm \sqrt {49 + 40}} {2}\\x = \frac {7 \sqrt {89}} {2}[/tex]
So, the roots are:
[tex]x_ {1} =\frac {7+ \sqrt {89}} {2}\\x_ {2} =\frac {7- \sqrt {89}} {2}[/tex]
Answer:
[tex]x_ {1} =\frac {7+ \sqrt {89}} {2}\\x_ {2} =\frac {7- \sqrt {89}} {2}[/tex]
