Question

Solve (x + 4)2 – 3(x + 4) – 3 = 0 using substitution. u = Select the solution(s) of the original equation.

Answer 1

To solve the given equation using substitution, define u as (x + 4), solve the quadratic equation for u, and then back-substitute to find the solutions for x.

Step-by-step explanation:

To solve the equation (x + 4)2 − 3(x + 4) − 3 = 0 using a substitution, we can let u = x + 4. This transforms our quadratic equation into u2 − 3u − 3 = 0, which is easier to solve.

Using the quadratic formula for an equation of the form au2 + bu + c = 0, we can calculate the solutions for u. Once we find the values of u, we substitute back to find the values of x by setting those values of u equal to x + 4 and solving for x.

In summary, the steps involved are:

1. Substitute u for (x + 4).
2. Solve the quadratic equation in terms of u.
3. Back-substitute to find the x values by equating u to x + 4.