Question

First factor the trinomial as a binomial square and then use the square root method to solve. Round the solution to the nearest tenth. x^2 - 14x + 49 = 3
A. {5.3, 8.7}
B. {4.8, 9.2}
C. {3.5, 7.5}
D. {6.2, 8.3}

Answer 1

Factoring:
binomial squares have certain rules they follow: for instance, (a+b)^2 = a^2 + 2ab +b^2 and (a-b)^2 = a^2 - 2ab + b^2. This problem looks like it follows the second rule. See if you can find a and b. Forget about the 3 when you do this

Answer 2

Ok creative you lost me

Answer 3

haha ok, my bad.
so basically, if you let x=a, you can relate my equation to (x-b)^2 = x^2 -14x +49. All you need to do now is figure out what b is. we know that the last term (49) is b^2. So you can just solve b^2=49 to find b

Answer 4

You follow?

Square Root Method:
once you get your b, your new factored equation will look something like this:
(x-b)^2 = 3 (only, with a number in b)
The square root method just means you take the square root of both sides so you get \[(x-b) = \sqrt{3}\]Then solve for x (because you should have gotten your b earlier)

Answer 5

ok

Answer 6

did you get b?

Answer 7

-14x

Answer 8

um, no not the term....i should have used different variables, sorry. From my equation b^2=49 b is 7 (plus or minus).

Answer 9

:/ lost me again/

Answer 10

ok, that's probably my fault. sorry!!
do you know what i was saying in my 2nd post?

Answer 11

No not really

Answer 12

Did you get the bit about the (a-b)^2 rule?

Answer 13

I would tell you just to use the quadratic formula to factor the equation, but the question doesn't want you to... it would have been easier to explain.

Answer 14

Yeah

Answer 15

Ok, what i did was to try to transform the given equation into that (a-b)^2 rule. Because the rule says the format should end up like a^2 - 2ab + b^2, and our equation began with x^2, I knew that a and x had to be the same. So I plugged x into a in the rule (so it looks like x^2 - 2bx + b^2). Then comparing the equations, you can see that they are different because of the 14 and the 49, right? You need to know what b is, so you set either 2bx=14 OR b^2=49, and solve. b should equal 7.

Answer 16

I hope that makes sense.
After you factor, you should get (x-7)^2. Now it's time to bring the 3 back in. Your equation should be (x-7)^2 = 3. Using the Square Root method just means take the square root of each side. If you square root (x-7)^2, you get x-7 and square-rooting 3 gives you \[\pm \sqrt{3}\]Now you solve for x. Add 7 to each side. You should then get 2 answers for x: \[x=7-\sqrt{3}\ OR\ x=7+\sqrt{3}\]
in decimal form that's x=5.26795 OR x=8.73205. One of the answers matches one of the answer choices above.

Answer 17

Ok thanx I have one more that I was wondering you if you could help me with?

Answer 18

sure. but this post is getting kind of long. Wanna make a new post?

Answer 19

ok