Question

Having a brainfreeze...
(x-2/3)^2 =14

Can someone help me with this? I would be so grateful :)

Answer 1

the inverse of raising a quantity to a power is taking the same root of it.

for example: \((\sqrt{x})^2=x\\(\sqrt[3]{87})^3=87\)

Answer 2

so it would just be x-2/3=14?

would I take the square root of 14, or just solve it?

Answer 3

take the square root of both sides to get rid of the ^2, yeah

Answer 4

Oh! ok, I remember now... Thank you so much!

Answer 5

feel free to post your answer here if you want it checked

anytime~

Answer 6

So I got x=sqroot14+ 2/3

is that right? Or is this one of those problems where I need to put a +_ in front?

Answer 7

\((\dfrac{x-2}{3})^2 =14\\\sqrt{(\dfrac{x-2}{3})^\cancel 2} =\pm\sqrt{14}\\\dfrac{x-2}{3}=\pm\sqrt{14}\\x-2= \pm 3\sqrt{14}\\x= 2+\pm 3\sqrt{14}\implies x=2+3\sqrt{14}\\x=2-3\sqrt{14}\)

Answer 8

Okay awesome. I think I got it. Thanks for explaining!

Answer 9

anytime

btw you can also do it by squaring out the terms individually. recall that a/b^2=a^2/b^2

Answer 10

and with that you can get http://www.wolframalpha.com/input/?i=%28x%5E2-4x%2B4%29%3D14*9
(x^2-4x+4)/9=14
(x^2-4x+4)=126
then solve that

Answer 11

Okay sweet! This has really helped a ton!