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Algebra Ch13 Test A Problem #13

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:


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



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Algebra Ch 15 Lesson 3 Number 5


I am in Algebra 1, Ch. 15, Lesson 3, # 5b. I have tried doing this in as many ways as I can think of and still have gotten the wrong answers. Mabey I am just missing something.


Have you looked at the solutions manual? When you are confused, that needs to be the first place you check. It usually shows how a problem is worked and while you  may have some questions about some of their steps, it usually can answer the “How do they get the answer?” question you’re asking.


To walk you through what is in the solutions manual here is what they do:


They start by getting a common denominator for those two fractions. They get the common denominator by multiplying the denominators.


They multiply both sides by x(x+2) (The common denominator)


Then they perform the distributive property and simplify.


Lastly, they perform some algebra (combining like terms and moving things around) until they get a quadratic equation. Then they use the quadratic formula (in your book on [pg. 719) to solve for x.


Then they use their calculator to get a decimal they can round to the appropriate place.


Take a look at the solutions manual along with these step by step instructions and you should get a good idea of what is going on in the problem. However, if after you’ve tried the problem again you still have questions I can add more clarification if you need.


I hope this helps!