Using complete sentences, explain how you would use the quadratic formula to solve x2 + 5x = -2. Why is the quadratic formula the best method to use?

Question

ankit042 · Answer

x^2 +5x +2 =0 now you can the formula to solve this equation

anonymous · Answer

Hey @genius12 help me out haha

hero · Answer

Naturally, when you have a quadratic equation of the form ax^2 + bx + c = 0, your first impulse might be to factor it. However, if you are not able to find two integers that multiply to get ac, yet add to get b, then you can use the quadratic formula to find the value of x. 

In other words, if solving:

     mn = ac
m + n = b

Does not yield to integers, m and n, then using the quadratic formula would be most appropriate:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

In the case of the quadratic equation $x^2 + 5x + 2 = 0$ we are not able to find two numbers that multiply to get -2, yet add to get 5. So we use the quadratic formula instead. Doing so, we get:

$$x = \frac{-5 \pm \sqrt{5^2 - 4(1)(2)}}{2(1)} = \frac{17 \pm 5}{2}$$

Which yields a non-integer value of x. This is our confirmation that the original quadratic was not factorable and using the quadratic formula was indeed necessary in this case.

anonymous · Answer

Thank so much Hero, haha you're my hero! :)

hero · Answer

I made a typo

$$x = \frac{\pm\sqrt{17} - 5}{2}$$

hero · Answer

But yeah, you're welcome.