Let u = x^2+ 3. Which equation is equivalent to (x^2+3)^2+ 21 = 10x^2+ 30 in terms of u?

Question

campbell_st · Answer

well factor the right hand side of the equation and you get 

$$(x^2 + 3)^2 + 21 = 10(x^2 + 3)$$

since $$u = x^2 + 3$$

the equation becomes 

$$(u)^2 + 21 = 10(u)$$

now just simplify

anonymous · Answer

Wait I typed in the equation incorrectly. I'm sorry. It was:
Let u = x^2+ 3. (x^2+3)^2+ 21 = 10(x^2+ 30)

anonymous · Answer

@campbell_st

anonymous · Answer

Wait no. I'm sorry give me a second

anonymous · Answer

Sorry! it was originally correct, but what happened to the 30?

campbell_st · Answer

ok then so the left side is straight forward

rewrite 

$$u = x^2 + 3~~~as~~~ x^2 = u - 3$$

so the right side becomes 

$$10(x^2 + 30) = 10([u^2 - 3] + 30)$$

hope that helps

campbell_st · Answer

oops should read 

$$10([u - 3] + 30)$$

anonymous · Answer

Okay I get it now! And the answer is u^2-10u+21?

campbell_st · Answer

well you have on the right side

10[u -3] + 30) = 10(u + 27) = 10u + 270

you can check to make sure

anonymous · Answer

woah.. you lost me now

campbell_st · Answer

the problem becomes

$$u^2 + 21 = 10([u - 3]  + 30) ~~~or~~~~u^2 + 21 = 10(u + 27)$$

so distribute and collect like terms.