Let m=x^(2)+3 Which equation is equivalent to (x^(2)+3)^(2) +7x^(2) +21=-10 A.) m^(2)-7m+10=0 B.) m^(2)-7m+31=0 C.) m^(2)+7m+10=0 D.) m^(2)+7m+31=0

Question

Let
`m=x^(2)+3`

Which equation is equivalent to
`(x^(2)+3)^(2) +7x^(2) +21=-10`

A.)
`m^(2)-7m+10=0`
B.)
`m^(2)-7m+31=0`
C.)
`m^(2)+7m+10=0`
D.)
`m^(2)+7m+31=0`

Answer 1

`{m}^(2) +7m + 28 = 0`

Explanation:

Given that,

`m = {x}^(2) + 3`

We know that,

`{x}^(2) = m- 3`

Now look at the sum

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

`( {x}^(2) + 3) ^(2) + 7 {x}^(2) + 21 = - 10 \\ {m}^(2) + 7 * m- 3 + 21 = - 10 \\ {m}^(2) +7m + 18= - 10 \\ {m}^(2) + 7m + 18+ 10 = 0 \\ {m}^(2) + 7m + 28 = 0`