Question #296de

1 Answer
Jan 8, 2018

Answer:

#x~~-2.31,-0.19#

Explanation:

First we square both sides:
#(sqrt(4)/sqrt(4x+9))^2=(sqrt(8x+2))^2#

#(sqrt(4))^2/(sqrt(4x+9))^2=(sqrt(8x+2))^2#

#4/(4x+9)=8x+2#

Now we can rearrange and make it eqial to 0:
#4=(8x+2)(4x+9)#
#(8x+2)(4x+9)-4=0#

Now expand brackets:

#(8x*4x)+(2*4x)+(8x*9)+(2*9)-4=0#

#32x^2+8x+72x+18-4=0#

#32x^2+80x+14=0#

We can remove out common factors:

#32x^2+80x+14=0#

#16x^2+40x+7=0#

#x=(-b+-sqrt(b^2-4ac))/(2a)#

#x=(-40+-sqrt(40^2-4(16*7)))/32#

#=(-40+-sqrt(1600-4(112)))/32#

#=(-40+-sqrt(1600-448))/32#

#=(-40+-sqrt(1152))/32#

#=(-40+sqrt(1152))/32or(-40-sqrt(1152))/32#

#~~-2.31or-0.19#