Question

The product of a positive number and that number decreased by 9 is 52. Write and solve an equation that models the sentence above.

Answer 1

a positive number: \(x\)
that number decreased by 9: \(x-9\)
product of a positive number and that number decreased by 9: \( x*(x-9)\)
product " " " " is 52:\( x(x-9) = 52\)

Solve \[x(x-9) = 52\]for \(x\). Make sure your solution is positive!

Answer 2

any ideas

Answer 3

ok so how would you solve that?

Answer 4

You could factor it, you could complete the square, you could use the quadratic formula, you could graph it...

Answer 5

Let's start by expanding and rearranging it a bit:
What do you get if you use the distributive property to get rid of the ( ), and move all of the terms to one side of the = sign?

Answer 6

you would get x^2-9=52

Answer 7

if you further simplify it it would be x^2=61

Answer 8

Uh, no, that would be wrong :-)

x(x-9) =

Answer 9

ohh ok then thanks

Answer 10

\[x(x-9)=\]
???

Answer 11

im confused :(

Answer 12

\[x(x-9) = x*x -9*x =\]

Answer 13

x^2-9x

Answer 14

That's better. So after we move the 52 to the other side, we have \[x^2-9x-52 = 0\]Which of the methods that I listed do you know?