How do you solve #x^2-2x-24=0# using the quadratic formula?

1 Answer
Feb 29, 2016

Answer:

#x = 6, -4#

Explanation:

The quadratic formula is:

#x = (-b +- sqrt(b^2 - 4ac))/(2a)#

and the general formula of a quadratic equation is:

#ax^2 + bx + c = 0#

With our current example, #x^2 - 2x - 24 = 0#, we know that our is already in the standard form hence we do not need to do any manipulations to compute for #x#.

[Solution]

#x^2 - 2x - 24 = 0#

We know that:
#a = 1#
#b = -2#
#c = -24#

Evaluating the quadratic equation with the values above...

#x = (-b +- sqrt(b^2 - 4ac))/(2a)#
#x = (-(-2) +- sqrt((-2)^2 - 4(1)(-24)))/(2(1))#
#x = (2 +- sqrt(4 + 96))/2#
#x = (2 +- sqrt(100))/2#
#x = (2 +- 10)/2#
#x = 12/2 , -8/2#
#x = 6, -4#

[Checking -> Using Factorisation]
#x^2 - 2x - 24 = 0#
#(x - 6)(x + 4) = 0#
#x = 6, -4#

Since we got the same answer for both method, we know that our answer is correct.