Grade 11 Math Help!?

Question

Okay, so We're doing Complete the Squares.
And I have an equation like this. I get stuck though.
H(T)=10t^2+300t+9750
H(t)=10(t^2-30t)+9750
Okay, here I get very confuzzeled.
How in the world do I get whats in the brakets
This is what the step after is..help.
H(t)=10(t^2-30t+225-225)+9570
Please tell me how I'm supposed to get to 225 in here. I don't understand at all.

I'm asking for help.
Not to be judged.
If you can't help me, then don't leave any comments that are rude or negative. That doesn't say anything nice about you.

Answer 1

H(t) = 10t² + 300t + 9750
H(t) = 10(t² + 30t ) + 9750

the 3rd term inside the () is (30/2)² = 225, so we add it inside the () and then subtract 10(225) outside the (), net change is +10(225) - 2250 = 0:

H(t) = 10(t² + 30t + 225) + 9750 - 2250
H(t) = 10(t + 15)² + 7500

from there you know vertex of parabola at (-15, 7500)
"brackets" uses ck, not just k

Answer 2

I notice your sign on 300t has changed from + to - in the next line... I will assume it is +, since it can't change... you must have typed something incorrectly...


H = 10t^2 + 300t + 9750

divide out the 10... you need a coefficient of 1 on the square term...

H = 10 ( t^2 + 30t) + 9750

now complete the square inside the (..)

step 1... ( 1/2 ) of 30 = 15, and step 2.... 15^2 = 225

so you need to add and subtract 225 inside the ( ...), that way, the value of the problem does not change... by adding 225, and subtracting 225 inside the (...), you have changed the (...) inside by zero... 225 - 225 = 0

thus H = 10 ( t^2 + 30t +225 - 225 ) + 9570

now bring out the -225, but it needs to multiplied by 10, due to the ' distributive law' ...

H = 10( t^2 + 30t + 225 ) - 2250 + 9750
or H = 10( t^2 + 30t + 225 ) + 7500

then H = 10 ( t + 15 )^2 + 7500

since ( t + 15 )^2 = t^2 + 2 * 15t + 225
**********************************

if by chance you meant

H = 10t^2 - 300t + 9750 , then process is the same, since (1/2) ( -30) = - 15, and (-15)^2 = 225

then H = 10 ( t^2 - 30t + 225 - 225) + 9750
H = 10 ( t^2 - 30t + 225 ) - 2250 + 9750
H = 10 ( t - 15 )^2 + 7500

notice the - 15 inside the (...), if you start with... -300t in the problem...

check... ( t - 15 )^2 = t^2 - 2*15t + ( -15)^2 =
t^2 - 30t + 225

Answer 3

The 225 comes from taking half of 30, which is 15, and squaring it (hence, completing the square).
The next step should actually read:
10(t^2 - 30t + 225) + 9750 - 10(225)
Reasoning: if you add 10(225) you must subtract 10(225).
Now you have:
10(t - 15)^2 + 7500.
You have completed the square.

Answer 4

you forgot to factor 10 out of 9750. When you do you have
975 inside the brackets too. subtract the 225 from 975
and you have 750 inside the brackets along with the 15^2

Answer 5

Dude, no way is that grade 11. You probably need a tutor if you can't solve those. That's basic algebra. You take that in 7th or 8th grade. Grade 11 is calculus. Get someone to help you with your math. (edit: Sorry if you thought I wasn't nice. I was just trying to give you some advice. I did leave an explanation.)

But just as an explanation: you get the 225 because 225-225=0 anyways. You just plug those numbers in so that you can "complete the square". Basically you're pulling them out of nothing because, in fact, they are equivalent to nothing. Hopefully that answered your question.

Answer 6

Ok first of all the second step is wrong it shouldnt be -30t. you have to take 10 t out of the bracket which will leave you with 10t(t-30).

Answer 7

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Answer 8

That is a good question .. There seems to be something missing! I am sorry I could not have been of more help.. kr