Solve for x, where x is a real number
3√ (x-2) -8 = 8

Could any1 please explain how to solve this step by step. I really want to be able to understand this. I already know x=274/9

Question

Solve for x, where x is a real number
3√ (x-2) -8 = 8

Could any1 please explain how to solve this step by step. I really want to be able to understand this. I already know x=274/9

jim_thompson5910 · Answer

Is the equation

$$\Large \sqrt[3]{x-2}-8 = 8$$

OR is the equation

$$\Large 3*\sqrt{x-2}-8 = 8$$

solomonzelman · Answer

(whatever it is)

$\normalsize\color{black}{ \sqrt[3]{x-2}-8=8}$
$\normalsize\color{black}{ \sqrt[3]{x-2}=0}$
$\normalsize\color{black}{ \sqrt[3]{x-2}=\sqrt[3]{0}}$
$\normalsize\color{black}{ x-2=0}$

$\normalsize\color{black}{3\sqrt{x-2}-8=8}$
$\normalsize\color{black}{ 3\sqrt{x-2}=0}$
$\normalsize\color{black}{ \sqrt{x-2}=0}$
$\normalsize\color{black}{ x-2=0}$

solomonzelman · Answer

It doesn't matter JT :)

jim_thompson5910 · Answer

true, didn't think that far ahead

anonymous · Answer

@jim_thompson5910 It's the first one

jim_thompson5910 · Answer

actually no

jim_thompson5910 · Answer

you have to add 8 to both sides, not subtract 8 from both sides

solomonzelman · Answer

Ohh, dang yeah... Silly mistake -:(

jim_thompson5910 · Answer

Did you get this far andreakristina?

$$\Large \sqrt[3]{x-2}-8 = 8$$

$$\Large \sqrt[3]{x-2}-8+8 = 8+8$$

$$\Large \sqrt[3]{x-2} = 16$$

anonymous · Answer

yes

jim_thompson5910 · Answer

what's the next step?

anonymous · Answer

@jim_thompson5910 oh wait my bad the 3 is actually multiplying the sqrt

jim_thompson5910 · Answer

so we have 

$$\Large 3*\sqrt{x-2} = 16$$

jim_thompson5910 · Answer

what's the next step?

anonymous · Answer

um, no idea. would we divide 3 from both sides,or do we sqrt the 16?? @jim_thompson5910

jim_thompson5910 · Answer

$$\Large 3*\sqrt{x-2} = 16$$

$$\Large \sqrt{x-2} = \frac{16}{3}$$

jim_thompson5910 · Answer

then we square both sides

we square both sides to get rid of the square root

jim_thompson5910 · Answer

$$\Large 3*\sqrt{x-2} = 16$$

$$\Large \sqrt{x-2} = \frac{16}{3}$$

$$\Large (\sqrt{x-2})^2 = (\frac{16}{3})^2$$

$$\Large x-2 = \frac{256}{9}$$

jim_thompson5910 · Answer

hopefully you see what the last step has to be?

anonymous · Answer

@jim_thompson5910 I add the two to the fraction correct. thank u so much i completely understand it now :)

jim_thompson5910 · Answer

correct, you add 2 to both sides

anonymous · Answer

@jim_thompson5910 could u help me with one more? 27^(2x)=9^(x-3)