How do you solve # x^2 - 2x + 1 = 0 # by factoring?

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Answer 1 · 2015-10-05T07:42:36

#color(blue)(x=1# is the solution for the equation.

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

After trying out a few numbers we get #N_1 = -1# and #N_2 =-1#
#-1*-1 = 1#, and #(-1)+(-1)= -2#

#x^2−color(blue)(2x)+1=x^2−color(blue)(1x-1x)+1#

#=x(x-1) -1 (x-1)#

#(x-1)(x-1)# , is the factorised form of the expression.

We now equate the factor to zero(both factors are equal).

#x-1=0, x=1#
#color(blue)(x=1# is the solution for the equation.