Question

Which of the following substitutions should be used to rewrite the equation 6(x + 5)² + 66 - 4 = 0 as a quadratic equation?

a) Let u = x + 5
b) Let u = x
c) Let u = 6(x + 5)²
d) Let u = 6x

Answer 1

The correct substitution to rewrite the given equation as a quadratic equation is u = x + 5. Apply this substitution to express the squared term as u², yielding a simpler quadratic in standard form.

Step-by-step explanation:

To rewrite the equation 6(x + 5)² + 66 - 4 = 0 as a quadratic equation, we should look for a substitution that simplifies the expression and makes it take on the general form ax² + bx + c = 0. The best choice for the substitution here would be u = x + 5. This substitution simplifies the equation because we can then express the squared term as u² which is characteristic of a quadratic equation.

Here's how you would apply the substitution:

• Let u = x + 5.
• Substitute u into the equation to get 6u² + 66 - 4 = 0.
• Simplify the constant terms to get 6u² + 62 = 0.
• Now, you have a quadratic equation in terms of u. To solve for u, you can use the quadratic formula if necessary.
• After finding the values for u, revert the substitution by replacing u with x + 5 to find the values for x.