Factoring:
This equation cannot be factored because its roots are irrational (as shown by solving with the quadratic formula). Also, to factor a quadratic equation, you need to find a pair of numbers whose product is equal to the c term (-5) and whose sum is equal to the b term (-6). There is no pair of numbers which satisfies this, further showing that the equation cannot be factored.
Quadratic Formula:
The quadratic formula is x=[tex]\frac{-b ± \sqrt{b^{2}-4ac } }{2a}[/tex].
First, you need to find the a, b and c terms of your equation. They are 1, -6, and -5 respectively.
Now, you must plug in to the equation and solve for x. You must do so twice, once with a plus sign in the numerator and once with a minus.
[tex]\frac{6 ± \sqrt{(-6)^{2}-4(1)(-5) } }{2(1)} \\\frac{6 ± \sqrt{36+20} }{2} \\\frac{6 ± \sqrt{56} }{2} \\\ \frac{6 ± 2\sqrt{14} }{2} \\3+\sqrt{14} \\3-\sqrt{14}[/tex]
The answers are 3+√14 and 3-√14.
Hope this helps!!
