Question

what substitution should be used to rewrite 6(x + 5)² + 5(x + 5) - 4 = 0 as a quadratic equation?
○ u = (x + 5)
○ u = (x - 5)
○ u = (x + 5)²
○ u = (x - 5)²

Explanation:

To rewrite the equation \(6(x + 5)^2 + 5(x + 5) - 4 = 0\) as a quadratic equation, we look for a substitution that replaces the repeated expression. The expression \((x + 5)\) appears in both the squared term and the linear term. Letting \(u=(x + 5)\) will transform the equation into \(6u^2+5u - 4 = 0\), which is a quadratic equation in terms of \(u\). The other options do not match the repeated expression in the original equation.

Answer:

A. \(u = (x + 5)\)