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

Answer 1

Eli Assouline

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

#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:

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

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

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

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Answer 2

Genesis Allen

#x=7#

#sqrt(x+9)=4#

Square both sides:

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

#rarrx+9=16#

#rarrx=16-9=7#

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Answer 3

Abigail Allen

To solve the equation sqrt(x+9) = 4, we need to isolate the variable x.

First, square both sides of the equation to eliminate the square root: (sqrt(x+9))^2 = 4^2.

This simplifies to x + 9 = 16.

Next, subtract 9 from both sides of the equation: x = 16 - 9.

Simplifying further, x = 7.

Therefore, the solution to the equation sqrt(x+9) = 4 is x = 7.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.