Question

How do you solve `x( x - 5) = 66`?

Answer 1

`x = 11 and -6`

Explanation:

`x(x-5) = 66`

`x^2-5x-66 =0`

`(x+6)(x-11) = 0`

`x+6 =0`

`x = -6`

and

`x - 11 =0`

`x = 11`

so: `x = 11 and -6`

Answer 2

`x=11`
`x=-6`

Explanation:

Given -

`x(x-5)=66`

`x^2-5x=66`

`x^2-5x+25/4=66+25/4=(264+25)/4=289/4`

`(x-5/2)^2=289/4`

`x-5/2=+-sqrt((289)/4)=17/2`

`x=17/2+5/2=22/2=11`

`x=11`

`x=-17/2+5/2=-12/2=-6`

`x=-6`

Answer 3

`x=-6,11`

Explanation:

Solve:

`x(x-5)=66`

Expand the left-hand side.

`x^2-5x=66`

Move all terms to the left-hand side.

`x^2-5x-66=0`

Factor the left-hand side.

Find two numbers that when added equal `-5` and when multiplied equal `-66`. The numbers `6` and `-11` meet the requirements.

`(x+6)(x-11)=0`

Solutions for `x`.

`x+6=0`

`x=-6`

`x-11=0`

`x=11`

`x=-6,11`