a) What are the values of #a# and #b# if #x^2+6x-3=(x+a)^2+b#? b) What is the value of #x# if #x^2+6x-3=0#?
There are several ways to solve this.
I will use a method called "completing the square".
First remove the constant from the variable side by adding
We want to turn the left side into a squared binomial.
So by adding
Re-writing the left side as a unexpanded squared binomial
and simplifying the right side:
Then using the square root property:
and finally subtracting