The equation you've provided, $ax^2 + bx + c = 0$, is a standard form of a quadratic equation where:

• $a$, $b$, and $c$ are constants,
• $x$ is the variable,
• $a \neq 0$ (if $a$ were 0, the equation would be linear, not quadratic).

Solving a Quadratic Equation

To solve this quadratic equation for $x$, you can use the quadratic formula:

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

Steps:

1. Identify the coefficients $a$, $b$, and $c$ from your equation.
2. Compute the discriminant $\Delta = b^2 - 4ac$:
   • If $\Delta > 0$, there are two distinct real roots.
   • If $\Delta = 0$, there is one real root (a repeated root).
   • If $\Delta < 0$, there are two complex roots.
3. Apply the quadratic formula to find the roots $x$.

Would you like to see an example, or do you have specific coefficients for $a$, $b$, and $c$ that you'd like to solve?

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Here are 5 related questions to expand on this topic:

1. What is the discriminant, and how does it determine the nature of the roots of a quadratic equation?
2. Can you derive the quadratic formula from completing the square?
3. How do the graphs of quadratic equations differ when the discriminant changes?
4. What is Vieta’s formula, and how does it relate to the sum and product of the roots of a quadratic equation?
5. How do you solve quadratic equations by factoring?

Tip: Always check the discriminant first to understand the nature of the solutions before applying the quadratic formula.