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#