Question

How do you solve `5x = \sqrt { 74x + 3}`?

Answer 1

`x=-1/25 color(white)("xxx")orcolor(white)("xxx")x=3`

Explanation:

If `5x=sqrt(74x+3)`
then
(after squaring both sides)
`color(white)("XXX")25x^2=74x+3`

(subtracting `74x+3` from both sides)
`color(white)("XXX")25x^2-74x-3=0`

(factoring)
`color(white)("XXX")(25x+1)(x-3)=0`

(leaving two possibilities)
#color(white)("XXX"){: (25x+1=0,color(white)("xx")orcolor(white)("xx"),x-3=0), (rarr x=-1/25,,rarrx=3) :}#

Answer 2

`x = -1/25, 3`

Explanation:

`5x = sqrt(74x + 3)`
`(5x)^2 = 74x + 3`
`25x^2 = 74x + 3`
`25x^2 - 74x - 3 = 0`

`x = (-b +- sqrt(b^2 - 4ac))/(2a)`
`x = (74 +- sqrt(-74^2 + 300))/50`
`x = (74 +- 76)/50`

`x = -1/25, 3`