How do you use factoring to solve this equation #x^2+x=56#?

1 Answer
May 23, 2015

#x^2+x=56#
#x^2+x - 56 = 0#

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*(-56) = -56#
and
#N_1 +N_2 = b = 1#

After trying out a few numbers we get #N_1 = 8# and #N_2 =-7#
#8*(-7) = -56#, and #8+(-7)= 1#

#x^2+x - 56 = x^2+8x - 7x - 56#
#x(x +8) - 7(x+8)#

#(x-7)(x +8)# is the factorised form

#color (red)(x = 7, x = -8# are the solutions for the expression.