You know when to use the quadratic equation when you're dealing with a quadratic equation of the form:

$ax^2 + bx + c = 0$

where:

• $a$, $b$, and $c$ are constants, and
• $x$ is the variable you're trying to solve for.

The key characteristic of a quadratic equation is the $x^2$ term (the variable is squared). If an equation has this squared term and can be rearranged into the above form, the quadratic formula can be applied:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Steps to determine if the quadratic equation is applicable:

1. Identify the degree of the equation: It should be a second-degree equation (highest power of $x$ is 2).
2. Check for the form: Ensure the equation can be rewritten in the general form $ax^2 + bx + c = 0$.
3. Use when factoring is hard or impossible: If factoring the equation is difficult, or the equation doesn't easily factor, the quadratic formula can be used to find the solutions.
4. Irrational or complex roots: The quadratic formula works even when the solutions are irrational or complex numbers (when the discriminant $b^2 - 4ac$ is less than zero).

Would you like more details on applying the quadratic formula?

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5 Related Questions:

1. What is the discriminant, and how does it affect the type of solutions in a quadratic equation?
2. How do you solve a quadratic equation by factoring?
3. Can all quadratic equations be solved by using the quadratic formula?
4. What are the steps for completing the square to solve quadratic equations?
5. How do we graph a quadratic equation, and what do the solutions represent on the graph?

Tip: Always check if a quadratic equation can be factored easily before using the quadratic formula—it can save time!