-5126 = -6 - 5(x+ 22)^(5/3)    solve the equation.

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hala718's profile pic

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

Posted on

-5126 = -6 - 5(x+ 22)^(5/3)

First we will add 6 to both sides:

==> -5120 = -5(x+22)^(5/3)

Now divide by -5:

==> 1024 = (x+ 22)^(5/3)

Now we know that 1024 = 2^10

==> 2^10 = (x+22)^5/3

Now we will raise both sides to the power (3/5)

==> (2^10)^3/5) = [(x+22)^5/3)]^3/5

==> We know that:

a^b^c = a^(bc)

==> 2^(10*3/5) = (x+ 22) ^1

==> 2^(6) = x+ 22

==> 64 = x+ 22

Now subtract 22 from both sides:

==> x= 64 - 22 = 42

==> x= 42

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll move -6 to the left side, changing it's sign;

 -5126+6 =  - 5(x+ 22)^(5/3) 

-5120 =  5(x+ 22)^(5/3) 

Since 5120 is divisible by 5, we'll divide by -5 both sides:

1024 = (x+ 22)^(5/3) 

We'll raise both sides to 3/5 power:

1024^(3/5) = x+22

We'll use the symmetric property and we'll subtract 22 both sides:

x = 1024^(3/5) - 22

x = 2^(10*3/5) - 22

x = 2^6 - 22

x = 64 - 22

x = 42

Since the order of the radical is odd, we don't have constraints for the value of the solution of the equation, so the value for x is accepted. 

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