How do you solve the equation #(4x-5)^2=64#?

2 Answers
Feb 27, 2017

Answer:

#x = 13/4#

Explanation:

Square root both sides of the equation and simplify:
#sqrt((4x-5)^2) = sqrt(64)#

#4x - 5 = 8#

#4x = 13#

#x = 13/4#

Feb 27, 2017

Answer:

#x=-3/4" or "x=13/4#

Explanation:

Take the #color(blue)"square root of both sides"#

#sqrt((4x-5)^2)=color(red)(+-)sqrt64#

#rArr4x-5=color(red)(+-)8#

#•"solve "4x-5=color(red)(+)8#

add 5 to both sides.

#4xcancel(-5)cancel(+5)=8+5#

#rArr4x=13#

divide both sides by 4

#(cancel(4) x)/cancel(4)=13/4#

#rArrx=13/4#

#• "solve "4x-5=color(red)(-8)#

#rArr4x-5+5=-8+5#

#rArr4x=-3#

#rArrx=-3/4#

#color(blue)"As a check"#

Substitute these values into the left side and if equal to the right side then they are the solutions.

#(cancel(4)^1xx13/cancel(4)^1-5)^2=8^2=64#

#(cancel(4)^1xx-3/cancel(4)^1-5)^2=(-8)^2=64#

#rArrx=-3/4" or "x=13/4" are the solutions"#