Question

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Let a = x^2 + 4. Rewrite the following equation in terms of a and set it equal to zero. (x^2 + 4)^2 + 32 = 12m^2 + 48 In resulting equation what is the coefficient of the a term? In the resulting equation, what is the constant?​

Answer 1

Answers:

• Coefficient of the 'a' term:  -12
• Constant term: 32

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Work Shown:

Let's isolate x^2

a = x^2 + 4

x^2 + 4 = a

x^2 = a - 4

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Then we'll apply substitution

(x^2+4)^2 + 32 = 12x^2 + 48

a^2 + 32 = 12x^2 + 48 ........... replace x^2+4 with 'a'

a^2 + 32 = 12(a-4) + 48 ......... replace x^2 with a-4

a^2 + 32 = 12a-48+48 ....... distribute

a^2 + 32 = 12a

a^2 + 32 - 12a = 0

a^2 - 12a + 32 = 0

The last equation is in standard form.

The coefficient of the 'a' term is -12 since it is the number to the left of the 'a'. We don't focus on a^2 here.

The constant term is the term without any variable attached, so the constant is 32.