Question

p(x)=-5x^2+400x-2550 repersents the profit made when x amount of money is spend on advertising

How much money should be spend on advertising to have a profit of atleast 4 000 000

Answer 1

Can someone explain how to solve this?

Answer 2

I tried to set p to 4 000 000 but then what do I do?

Answer 3

\[
-5x^2+400x-2550=4 000 0
\]

Answer 4

Subtract \(4 000 0\) and use the quadratic equation.

Answer 5

its 4 000 000

Answer 6

It there another way other than the quadratic equation?

Answer 7

Partal Factoring?

Answer 8

You can complete the square.

Answer 9

But then the x value stays 40? which is not right

Answer 10

\[-5x^2+400x-2550=4000000\]

\[5x^2-400x+2550=-4000000\]
\[5x^2-400x+4002550=0\]
\[x^2-80x+800510=0\]

Answer 11

how did you get 800510?

Answer 12

Did you notice that I divided both sides of the equation by 5?

Answer 13

whats next?

Answer 14

Something is wrong with your posting because that equation has only imaginary roots.

Answer 15

its 4000

Answer 16

Not 4000 000 the question said in thousands but then we make millions

Answer 17

so its really 4000

Answer 18

Well...that should make a significant difference.

Answer 19

sorry

Answer 20

That equation has real roots but it will not factor so plug it into the quadratic formula.

Answer 21

so we have no choice but to use the quadracic formuula... the lesson we are learning is partial factoring i was guessing it would be related somehow?

Answer 22

Yes. You could use partial factoring.

Answer 23

Could you explain how?

Answer 24

because I am always getting 40 as the x value

Answer 25

-5((x-80)x+510)=4000

Answer 26

-5x^2+400x-2550-4000
-5x^2+400x-6550
-5x(x-80)-6550

and then the x value is 40 80/2 - 40...

Answer 27

What is wrong?

Answer 28

I don't see how you get the x value of 40 from what you have posted.

Answer 29

What should x be then?

Answer 30

in partial factoring dont we divide p/2 to give us the x value for the vertex?

Answer 31

Can you show how to find x? please

Answer 32

http://www.wolframalpha.com/input/?i=%E2%88%925x^2%2B400x%E2%88%922550%3D4000

Answer 33

how can this be solved by partial facotring...???

Answer 34

Perhaps that is not what is meant by partial factoring. Let me google it and see.

Answer 35

Ill ask my teacher then...its ok

Answer 36

\[-5x^2+400x-2550=4000\]
\[-5x2+400x-6550=0\]
\[5x^2-400x+6550=0\]
\[x^2-80x+1310=y\]
Let y = 1310
x(x-80)=0
x=0, x=80

Answer 37

partial factoring means bringing into vertex form
a(x+h)^2+k

Answer 38

for solving quadratics using graphs

Answer 39

Ill confirm with my teacher on monday thanks for your help @Mertsj

Answer 40

yw