How do you solve #5x^2 - 7x - 6 = 0# by factoring?

1 Answer
Aug 12, 2015

Answer:

The solutions are

#color(blue)(x=-3/5#
#color(blue)(x=2 #

Explanation:

#5x^2−7x−6=0#

We can Split the Middle Term of this expression to factorise it and thereby find the 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 = 5*-6 = -30#
and
#N_1 +N_2 = b = -7#

After trying out a few numbers we get #N_1 = -10# and #N_2 =3#
#-10*3 = -30#, and #3+(-10)= -7#

#5x^2−color(blue)(7x)−6= 5x^2−color(blue)(10x +3x)−6#

#= 5x(x-2) + 3(x-2)#

#color(blue)((5x+3)(x-2) # are the factors of the expression.

Now we equate these factors to zero and find the solutions:

#5x+3 = 0 , color(blue)(x=-3/5#
#x-2 =0, color(blue)(x=2 #