How do you solve #x^2-2x=8#?

1 Answer
Sep 12, 2015

Answer:

#color(blue)(x=-2#
# color(blue)(x=4#

Explanation:

#x^2−2x- 8 = 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 = 1*-8 = -8#
AND
#N_1 +N_2 = b = -2#

After trying out a few numbers we get #N_1 = -4# and #N_2 =2#
#2*(-4) = -8# and #2 + (-4)= -2#

#x^2−2x- 8 = x^2 color(blue)(- 4x + 2x)- 8#

#= x( x-4) + 2(x - 4)#

#color(blue)((x+2) ( x-4)# is the factorised form for the expression, we now equate the factors to zero and obtain the solutions.

#x+2 = 0, color(blue)(x=-2#
#x-4 = 0, color(blue)(x=4#