How do you solve #x^2 +3x - 18 = 0# by factoring?

Question

39822 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-29T12:59:01

The solutions are

# color(blue)(x=3#

# color(blue)(x=-6#

#x^2+3x-18#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*-18 = -18#

AND

#N_1 +N_2 = b = 3#

After trying out a few numbers we get #N_1 = 6# and #N_2 =-3#

#6*-3 = -18#, and #6+(-3)= #

#x^2+3x-18 = x^2+6x-3x-18#

#x(x+6) -3(x+6)=0#

#(x-3)(x+6) =0#

Now we equate the factors to zero to obtain the solutions:

#x-3 = 0, color(blue)(x=3#

#x+6 = 0, color(blue)(x=-6#