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[tex](x^2+3)^2 + 7x^2+21=-10[/tex]

We want to convert this equation in terms of m, where [tex]m = x^2+3[/tex]

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

[tex]m^2 + 7x^2+21=-10[/tex]

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

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

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

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

wegnerkolmp2741o

Answer:

m^2 +7(m) = -10

m^2 + 7m +10=0

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

Are all acceptable versions of the equation

Step-by-step 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)

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