Question from Grace:
We are using this test A as a practice test. We can’t figure out how to solve this.
Answer from Dr. Callahan:
Grace,
To solve this one, you take the square root of each side
+/- SQRT ( 16x^2 + 8x +1 ) = +/- SQRT (9)
The left side needs a little work to do this. Best to see if we can factor
16x^2 + 8x +1
As a hint, you know your factors would need to be the same since you are taking a square root.
So start with the first term 16x^2 – square root of it is 4x. So try that
(4x + ___) (4x + ___)
Then the last term is 1. So the obvious thing that can be multiplied by itself to get 1 is 1. So try
(4x + 1) (4x + 1)
Now when I multiply is out I get
16x^2 + 4x + 4x + 1 = 16x^2 + 8x +1
So that works!!
Now back to the problem
+/- SQRT ( 16x^2 + 8x +1 ) = +/- SQRT (9)
+/- SQRT ((4x + 1) (4x + 1)) = +/- SQRT (9)
Using the + we have
(4x + 1) = 3
And 4x = 2 so x = 1/2 is one answer
Using the – we have
(4x + 1) = -3
4x+1 = -3
4x = -4
x = -1
