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

2 Answers
Feb 25, 2018

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) :}

Feb 25, 2018

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