How do you factor and solve #x^2+x-20=0 #?

1 Answer
May 20, 2016

Answer:

The solutions are # x = 4, x=-5#

Explanation:

#x^2 + x - 20 = 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* (-20) = -20#

AND

#N_1 +N_2 = b = 1#

After trying out a few numbers we get #N_1 = -4# and #N_2 =5#
#(-4)*5 = -20#, and #5+(-4)= 1#

#x^2 + x - 20 = x^2 + 5x -4x - 20 #

# = x(x+5) - 4(x + 5)#

#(x+5)# is a common factor to each of the terms

#=color(green)((x-4)(x+5)#

We equate both factors to zero and obtain the solutions:

  • #x-4 = 0 , x = 4#
  • #x+5 = 0, x=-5#