How long does it take the giraffe to weigh 85 kg?

[Paulo2014]

Homework Statement

The weight, W kg, of a giraffe over its first two years of life, is given by the equation
W=(t^2)/4-t+68
where t is the time in months since the giraffe was born.
How long does it take the giraffe to weigh 85 kg?

Homework Equations

The Attempt at a Solution

I know i need to rearage the equation but i can't remember how so any help is appreciated...

 

[happyg1]

Which letter represents the weight? Put 85 there and solve it.

 

[Paulo2014]

Yeah I understand that but how would I solve it?

its the (t^2)/4 bit i don't understand how to solve...

 

[happyg1]

Let me see if this is the thing you have:
$$\frac{t^2}{4}-t+68=85$$
That's a quadratic equation. Before you can solve, what does the equation have to look like?
Then, since fractions give me a headache, like like to ditch them. Can you think of a method of getting rid of them?

 

[Paulo2014]

multiply 4 to both sides?

 

[happyg1]

Yes please.

 

[Paulo2014]

So it would be:
t^2-t+68=340?

 

[happyg1]

so you have:
$$4(\frac{t^2}{4}-t+68=85)$$
make sure that you are careful about your distributive property.
EVERYTHING gets multiplied by 4.

 

[Paulo2014]

but doesn't the t^2 already have the /4 so wouldn't it be:

t^2+4(-t+68=85)?

 

[happyg1]

yes
$$4(\frac{t^2}{4}-t+68=85)$$
$$t^2-(4)t+(4)68=(4)85$$
then what?

 

[Paulo2014]

expand.

So it is t^2-4t+272=340

Is that right?

 

[happyg1]

yes.
In order to solve ANY equation, what does it have to be set equal to?
There's ONE MORE STEP before you can solve it.

 

[Paulo2014]

I can't remember... :(

 

[rocomath]

Look for an example in your book.

 

[Paulo2014]

It has to be in the form ax=b

thats what my textbook says... is that what you meant?

 

[happyg1]

You are looking for the ZEROS
What would you set the equation equal to to get the ZEROS?

 

[Paulo2014]

i'm lost...

 

[happyg1]

In order to solve any equation, it must be set equal to ZERO!
HOORAY!
How do you manipulate your equation to get it equal to zero?

 

[Paulo2014]

I see. take 340 from both sides so the equation is:t^2-4t-68=0 is that correct?

 

[rocomath]

Sit down and read the chapter ... do every single example problem! It will serve you better than trying to solve this problem.

 

[happyg1]

rocomath is right.
and you did get the equation right. If you aren't sure how to solve it, you DO need to read the chapter.

 

[Paulo2014]

I use the quadratic formula don't I...

 

[happyg1]

yes you do

 

[Paulo2014]

I got x=10.48528137423857 or -6.4852813742385695

 

[Paulo2014]

Is that right?

 

[rocomath]

https://www.physicsforums.com/showpost.php?p=1668913&postcount=5

 

[Paulo2014]

t has to equal 10.5 as you can't have a negative amount of years right?

 

[Tedjn]

Yes, the negative answer is extraneous.

 

[HallsofIvy]

No, that's not what he is talking about.

happyg1, you don't have to set an expression to 0 to solve an equation. Here, of course, you could subtract 340 from both sides to get x²- 4t- 68= 0 and try to factor. However, I don't think it will be so easy to factor this.

My favored way of solving x²-4t+ 272=340 would be to subtract 272 from both sides: x²- 4t= 68 and then complete the square.

 

[Paulo2014]

So is my answer incorrect?