Welcome to this week's lesson on Solving Quadratic Equations using Square Roots. Below you will find a summary of the concepts covered in class, detailed examples from the notes, and the homework schedule for the week.

Key Concepts: The Square Root Property

When solving an equation where the variable is squared (like $x^2$) or part of a squared group (like $(x+3)^2$), we can use the Square Root Property. Here is the step-by-step process we practiced in class:

  1. Isolate the Squared Term: Get the $x^2$ or the parenthesis group by itself on one side of the equation.
  2. Take the Square Root: Take the square root of both sides to cancel out the square.
  3. Remember the Plus/Minus ($\\pm$): This is crucial! When you take the square root of a variable squared, the answer can be positive or negative.
  4. Simplify the Radical: Use factor trees to break down non-perfect squares (e.g., $\\sqrt{40}$ becomes $2\\sqrt{10}$).

Examples from Class Notes

Here are a few examples we worked through in the attached notes:

1. Simple Quadratic:

$$x^2 - 100 = 0$$ $$x^2 = 100$$ $$x = \\pm\\sqrt{100}$$ $$x = \\pm 10$$

2. Simplifying Radicals:

$$x^2 - 40 = 0$$ $$x^2 = 40$$ $$x = \\pm\\sqrt{40}$$

(Using a factor tree, we know $40 = 4 \\cdot 10$, and the square root of 4 is 2)

$$x = \\pm 2\\sqrt{10}$$

3. Binomial Squared:

$$(x+5)^2 = 9$$ $$\\sqrt{(x+5)^2} = \\sqrt{9}$$ $$x + 5 = \\pm 3$$

(This splits into two equations: $x+5=3$ and $x+5=-3$)

$$x = -2 \\text{ or } -8$$

Homework Assignment

Please refer to the attached Worksheet: Solving Quadratic Equations: Square Root Law. The assignment is split over two days:

  • Part 1: Problems #1-10
  • Part 2: Problems #11-20
  • Due Date: The full homework packet is due on Monday, April 21st.

Important Announcements

Due to my absence on Thursday afternoon and Friday, there will be no quiz on Monday. Instead, I will be grading 5 random questions from the homework assignment to count as a quiz grade. Please ensure all your work is shown clearly!

If you are struggling with these concepts, I highly recommend reviewing the relevant topics on Khan Academy or watching the supplementary videos posted below. If you do not completely understand the material, please come and ask for help!