How do you solve #x^2 + 5x – 6 = 0#?

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Answer 1 · 2015-08-20T13:42:55

The solutions are

#color(green)(x=-6#

# color(green)(x=1#

# x^2+5x–6=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*-6 = -6#

and

#N_1 +N_2 = b = 5#

After trying out a few numbers we get :

#N_1 = -1# and #N_2 =6#

#6*-1 = -6#, and #6+(-1)= 5#

# x^2+5x–6= x^2+6x-1x–6#

#x(x+6)-1(x+6)=0#

#(x+6)# is a common factor to each of the terms

#color(green)((x+6)(x-1)=0#

We now equate factors to zero:

#x+6=0, color(green)(x=-6#

#x-1=0, color(green)(x=1#