Question

Question #d2d79

Answer 1

`x = 65+sqrt2125 = 111.1`

`x= 65-sqrt2125 =18.9`

Explanation:

You have got to the step of `1425 = (125-x)(x-5)`

Now get rid of the brackets, and you will end up with an `x^2` term.
That means it is a quadratic equation.

Make it equal to `0` and then decide on an appropriate method of solving..

• factorising
• completing the square
• quadratic formula

`color(white)(xxxxxxxxxxxxx)1425 = (125-x)(x-5)`

`color(white)(xxxxxxxxxxxxx)1425 = 125x-625 -x^2 +5x`

`x^2 -130x +625 + 1475 =0`

`color(white)(xxxxx) x^2-130x +2100 =0`

Complete the square:

`x^2 -130x color(white)(xxxx) = -2100" "larr ((-160)/2)^2 = 65^2`

`x^2 -130x +65^2 = -2100 +65^2`

`(x-65)^2 = 2,125`

`x-65 = +-sqrt2125`

`x = 65+sqrt2125 = 111.1`

`x= 65-sqrt2125 =18.9`