Dimitri is solving the equation #x^2 - 10x = 21#. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?
1 Answer
Jan 23, 2016
25
Explanation:
To make the left side a perfect square - have to 'complete the
square' .
# ( 1/2 color(black)("coefficient of x-term "))^2 # is required to be added to complete the square
In this case
# 1/2 of (-10) = - 5 , (-5)^2 = 25# This then must be added to both sides to retain 'balance'
#rArr x^2 - 10x + 25 = 21 + 25 #
# rArr (x - 5 )^2 = 46 # There is now a perfect square on the left side .
