How do you solve #sqrt (x+9)=4#?

2 Answers
Jan 27, 2016

Answer:

To solve equations that involve radicals, you must square both sides of the equation.

Explanation:

#sqrt(x + 9)# = 4

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

x + 9 = 16

x = 16 - 9

x = 7

With radical equations it is alway vital to check your solutions in the original equation, since extraneous solutions may arise. You must especially be careful of them in radical-quadratic equations, where two solutions often appear but oftentimes only one is the correct solution.

Practice exercises:

  1. Solve each equation. Watch out for extraneous solutions.

a) #sqrt(2x + 5)# = 7

b) #sqrt(3x + 1)# = x - 3

c) #sqrt(2x + 2)# - #sqrt(x +2)# = 1

Jan 30, 2016

Answer:

#x=7#

Explanation:

#sqrt(x+9)=4#

Square both sides:

#rarr(sqrt(x+9))^2=4^2#

#rarrx+9=16#

#rarrx=16-9=7#