How do you solve #x^2 + 2x - 15 = 0# by factoring?

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Answer 1 · 2015-08-16T17:13:23

The solutions are
# color(blue)(x=3#

#color(blue)(x=-5#

# x^2+2x−15=0#

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

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*-15 = -15#
AND
#N_1 +N_2 = b = 2#

After trying out a few numbers we get #N_1 = 5# and #N_2 =-3#
#5*-3 = -15#, and #5+(-3)= 2#

# x^2+2x−15=x^2+5x-3x−15#

#x(x+5) -3(x+5)=0#

#(x-3)(x+5) =0#

Now we equate the factors to zero to find the solutions:
#x-3 =0, color(blue)(x=3#

#x+5 =0, color(blue)(x=-5#