Question

9)

Seventy-five times a negative integer minus 36 equals 21 times the square of the negative integer. Which equation could be used to solve for the unknown negative integer?

Answer 1

`21 x^2 +75 x+36 =0`

Explanation:

Let us assume that the negative integer is -x

Now we have

Seventy - five times a negative integer =
`75 (-x ) = -75 x`

Seventy - five times a negative integer minus 36 =
`-75x - 36`

Square of negative integer =
`(-x)^2 = x^2`

21 times the square of negative integer =
`21 x^2`

Now it is given that

Seventy - five times a negative integer minus 36 is equal to 21 times the square of negative integer

So we have

`-75x -36 = 21 x^2`

We can also try to write this in standard form by bring all the terms to one side

`-75x = 21 x^2 +36` ( adding 36 to both sides)

`0 = 21 x^2 +75 x+ 36` ( adding 75x to both sides )

`21 x^2 +75 x+36 =0` ( Answer )