Solve for x (x^2-9)^1/2=4

3 Answers | Add Yours

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

(x^2 -9)^1/2 = 4

First we will square both sides:

==> ((x^2 -9)^1/2)^2 = 4^2

==> (x^2 -9) = 16

Now add 9 to both sides:

==> x^2 = 25

==> x= +-5

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To eliminate the square root, we'll raise to square both sides of the equation:

[( x^2 - 9)^(1/2)]^2 = 4^2

We'll eliminate the square root from the left side :

x^2 - 9 = 16

We'll add 9 both sides:

x^2 = 25

x1 = +sqrt25

x1 = 5

x2 = -5

We'll verify the solutions into equation:

sqrt(25-9) = 4

sqrt16 = 4

4 = 4

sqrt((-5)^2-9) = 4

sqrt(25-9) = 4

4 = 4

The equation will have 2 solutions, x=5 and x2=-5.
neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve for (x^2-9)^(1/2) = 4.

Square both sides.

x^2-9 = 4^2 = 16

x^2 = 16+9 .

x^2 =25

x^2-5^2  = 0.

(x-5)(x+5) = 0.

x-5 =0, x+5 = 0

x=5 ,or x= -5.

 

We’ve answered 318,911 questions. We can answer yours, too.

Ask a question