How do you factor #x^2 - x = 72#?

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Answer 1 · 2016-05-04T17:50:55

#color(green)(( x+8) ( x - 9) # is the factorised form of the expression.

#x^2 - x = 72#

#x^2 - x - 72 = 0#

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*(-72) = -72#

AND

#N_1 +N_2 = b = -1#

After trying out a few numbers we get #N_1 = -9# and #N_2 =8#
#8*(-9) = -72#, and #8+(-9)= -1#

#x^2 - x - 72 = x^2 - 9x +8x - 72 #

#= x ( x - 9) + 8 (x - 9 ) #

#= color(green)(( x+8) ( x - 9) #