Question

Please solve y=x^2-6x-5 by factoring and by using the quadratic formula with work attached

Answer 1

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=$\frac{-b ± \sqrt{b^{2}-4ac } }{2a}$.

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.

$\frac{6 ± \sqrt{(-6)^{2}-4(1)(-5) } }{2(1)} \\\frac{6 ± \sqrt{36+20} }{2} \\\frac{6 ± \sqrt{56} }{2} \\\ \frac{6 ± 2\sqrt{14} }{2} \\3+\sqrt{14} \\3-\sqrt{14}$

The answers are 3+√14 and 3-√14.

Hope this helps!!