Hello! I'm doing well, thank you for asking! I'd be happy to assist you with your child's Algebra lesson on Solving Simple Quadratic Equations. Let's break it down to ensure a thorough understanding.

What is a Simple Quadratic Equation?

A quadratic equation is an equation of the form:

$ax^2 + bx + c = 0$

Where:

• $a$, $b$, and $c$ are constants,
• $x$ is the variable to be solved,
• $a \neq 0$ (because if $a = 0$, it becomes a linear equation).

The most common methods to solve simple quadratic equations:

1. Factoring: Works when the quadratic can be factored easily.

   • Example: $x^2 - 5x + 6 = 0$ can be factored into $(x - 2)(x - 3) = 0$.

2. Using the Square Root: Useful when the equation has no linear term ($b = 0$).

   • Example: $x^2 = 9$, take the square root of both sides: $x = \pm3$.

3. Completing the Square: Used to transform the equation into a perfect square trinomial.

   • Example: $x^2 + 6x = 7$, you add 9 (half of $6$, squared) to both sides.

4. Quadratic Formula: Applicable to all quadratic equations, the formula is:

   $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ This gives the exact solutions for any quadratic equation.

Example Problem (Factoring):

Solve $x^2 - 7x + 10 = 0$.

Step 1: Factor the quadratic expression: $x^2 - 7x + 10 = (x - 2)(x - 5)$.

Step 2: Set each factor equal to 0: $x - 2 = 0 \quad \text{or} \quad x - 5 = 0$

Step 3: Solve for $x$: $x = 2 \quad \text{or} \quad x = 5$

The solutions are $x = 2$ and $x = 5$.

Would you like more examples or explanations on specific methods, or do you want to go over some problems your child has worked on?

5 Related Questions:

1. Can you explain how to solve a quadratic equation by completing the square?
2. How does the discriminant in the quadratic formula help determine the type of solutions?
3. What are the conditions for factoring to be the best method to solve a quadratic equation?
4. Could you explain solving quadratic equations with no real solutions?
5. How does solving quadratic equations relate to graphing parabolas?

Tip:

Always check if a quadratic can be factored easily before using more complex methods like the quadratic formula. It saves time!