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

2 Answers
marfre
Feb 27, 2017

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

Jim G.
Feb 27, 2017

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"

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