a) What are the values of aa and bb if x^2+6x-3=(x+a)^2+bx2+6x−3=(x+a)2+b? b) What is the value of xx if x^2+6x-3=0x2+6x−3=0?
1 Answer
a)
b)
Explanation:
Part a
Part b
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.
Remember that
So if
then
and
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