Need help with factoring and solving: (15/16x+1)^2=16

[mathchallenged1]

the problem is (15/16x+1)^2=16

I know that I have to square root both sides somehow but past that point I really don't know. I thought that I had the answer before but it turned out to be wrong. The real problem is the fraction 15/16x. I'm having real problems with this equation can anyone help??? any advice would be great. thank you

 

[stapel]

the problem is (15/16x+1)^2=16

As posted, this means:

. . . . .[15/(16x) + 1]² = 16

Is this what you meant?

Also, if this is a "factor to solve" problem, why not try factoring, rather than taking roots? Move the 16 over to the left-hand side, apply the difference-of-squares factoring formula, and solve the resulting factors.

Eliz.

 

[mathchallenged1]

the only thing that is wrong with the problem you set up is the (16x) if I'm not mistaken then the X factor applies to the 15/16 fraction, but other than that, yes that is what I ment (sorry I'm new at this). I'm really bad at math equations like this. what do you mean by getting rid of the fraction? I can see moving the 16 to the other side but (difference-of-squares)??? you have totally lost me

 

[stapel]

the only thing that is wrong with the problem you set up is the (16x) if I'm not mistaken then the X factor applies to the 15/16 fraction

So you meant the following...?

. . . . .[(15/16)x + 1]² = 16

what do you mean by getting rid of the fraction?

I have no idea; did I say something about that...?

...difference-of-squares? you have totally lost me

The "difference of squares" formula should have been covered (back in factoring) long before the class got to "solving". To review, try studying one or another of the lessons available online. But the short version is:

. . . . .a² - b² = (a + b)(a - b)

Applied to the top-most equation, you'd get [(15/16)x + 1] + (something) and [(15/16)x + 1] - (something) equalling zero. Then solve these linear equations.

Eliz.

 

[Denis]

the problem is (15/16x+1)^2=16
I know that I have to square root both sides somehow but past that point I really don't know. I thought that I had the answer before but it turned out to be wrong. The real problem is the fraction 15/16x. I'm having real problems with this equation can anyone help??? any advice would be great. thank you

15/16x means 15 divided by 16, then multiplied by x;
if 15/16x is a fraction, then MUST be shown this way: 15/(16x).

Also, you DO NOT square both sides; you multiply out the left side;
remember that n^2 = n times n;
so (15/(16x) + 1) times (15/(16x) + 1) = 225/(256x^2) + 30/(16x) + 1; so:
225/(256x^2) + 30/(16x) + 1 = 16
225/(256x^2) + 30/(16x) - 15 = 0

Now, to get rid of fractions, multiply through by 256x^2:
225 + 30(16x) - 15(256x^2) = 0

I'll let you finish it.

 

[mathchallenged1]

the teacher who I'm taking the class goes really fast so it probably was covered and I just missed it somewhere. I've just been having problems with this equation for some reason. thank you all for your help.

 

[Mrspi]

the problem is (15/16x+1)^2=16

I know that I have to square root both sides somehow but past that point I really don't know. I thought that I had the answer before but it turned out to be wrong. The real problem is the fraction 15/16x. I'm having real problems with this equation can anyone help??? any advice would be great. thank you

Ok...let's not overcomplicate things.

I assume you mean this:

[ (15/16)x + 1 ]<SUP>2</SUP>= 16

Take the square root of both sides:

(15/16)x + 1 = +/- 4

So,
(15/16) x + 1 = 4, or (15/16)x + 1 = -4

OR,

(15/16) x = 3 or (15/16) x = -5

Multiply both sides of each equation by (16/15):

(16/15)(15/16)x = (16/15)*3
or
(16/15)(15/16)x = (16/15)*(-5)

x = 16/5 or x = -16/3