Question

What is the factored form of the expression?

d^2 = 36d + 324

Answer 1

`(x-43.45)(x+7.45)=0`

Explanation:

We have the quadratic equation
`d^(2)=36d+324` i.e.
`d^(2)-36d-324=0`

As, the roots of the quadratic equation
`ax^(2)+bx+c=0` are given by
`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`.

So, from the given equation, we have,

a = 1, b = -36 , c = -324.

Substituting the values in
`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`, we get,

`x=\frac{36\pm \sqrt{(-36)^(2)-4* 1* (-324)}}{2* 1}`

i.e.
`x=(36\pm √(1296+1296))/(2)`

i.e.
`x=(36\pm √(2592))/(2)`

i.e.
`x=(36\pm 50.9)/(2)`

i.e.
`x=(36+50.9)/(2)` and
`x=(36-50.9)/(2)`

i.e.
`x=(86.9)/(2)` and
`x=(-14.9)/(2)`

i.e. x = 43.45 and x = -7.45

Thus, the roots of the equation are 43.45 and -7.45.

Hence, the factored form of the given expression will be
`(x-43.45)(x+7.45)=0`