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)} \\(6 ± √(36+20) )/(2) \\(6 ± √(56) )/(2) \\\ (6 ± 2√(14) )/(2) \\3+√(14) \\3-√(14)`

The answers are 3+√14 and 3-√14.

Hope this helps!!