How do you solve the equation #5(x-4)^2=125#?

1 Answer
May 5, 2017

Answer:

#x=-1" or " x=9#

Explanation:

#color(blue)"Isolate " (x-4)^2" by dividing both sides by 5"#

#(cancel(5)(x-4)^2)/cancel(5)=125/5#

#rArr(x-4)^2=25#

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

#sqrt((x-4)^2)=color(red)(+-)sqrt25larr" note plus or minus"#

#rArrx-4=+-5#

#"add 4 to both sides"#

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

#rArrx=4+-5#

#rArrx=4+5=9" or " x=4-5=-1#

#color(blue)"As a check"#

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

#x=-1to5(-1-4)^2=5xx5^2=125#

#x=9to5(9-4)^2=5xx5^2=125#

#rArrx=-1" or " x=9" are the solutions"#