How do you solve #X ( X+9) = 4 (X+6)# by factoring?

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Answer 1 · 2015-08-21T07:31:14

The solutions are
#color(blue)(X=3#
#color(blue)(X=-8#

#X(X+9)=4(X+6)#

#X^2+9X=4X+24#

#X^2+5X-24=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*-24 = -24#
AND
#N_1 +N_2 = b = 5#

After trying out a few numbers we get #N_1 = 8# and #N_2 =-3#
#8*-3 = -24#, and #8+(-3)= 5#

#X^2+5X-24=X^2+8X-3X-24#

#X^2+8X-3X-24=0#

#X(X+8) -3(X+8)=0#

#(X-3)(X+8)=0#

We now equate factors to zero.
#X-3=0, color(blue)(X=3#
#X+8=0, color(blue)(X=-8#