Question

Hello there!

If you can help me solve this equation step by step, that would be very helpful.

Thanks for stopping by!

Answer 1

`(x^2+3)^2 + 7x^2+21=-10`

We want to convert this equation in terms of m, where
`m = x^2+3`

While solving this problem, I instantly noticed the
`x^2+3` in the first term of the equation. Replace that with m.

`m^2 + 7x^2+21=-10`

Simplifying the rest is not as obvious. Using the distributive property, we can change
`[7x^2+21]` to
`[7(x^2+3)]`

Do you see the "m" in here? Look again if you don't.

Now we can simplify the equation to
`m^2 + 7m=-10` and this cannot be simplified further.

I'm always happy to help someone who appreciates the help! :D

Answer 2

m^2 +7(m) = -10

m^2 + 7m +10=0

(m+5) (m+2) =0

Are all acceptable versions of the equation

Explanation:

(x^2 +3) ^2 + 7x^2 +21 = -10

(x^2 +3)^2 + 7( x^2+3) = -10

Replace x^2 +3 with m

m^2 +7(m) = -10

Add 10 to each side

m^2 + 7m +10=-10+10

m^2 + 7m +10=0

Factor

(m+5) (m+2) =0

Using the zero product property

m=-5 m=-2

Replace m with x^2 +3

x^2+3 = -5 x^2 +3 =-2

Subtract 3 from each side

x^2+3-3 = -5-3 x^2 +3-3 =-2-3

x^2 = -8 x^2 = -5

x = ±2isqrt(2) x = ±i sqrt(5)