Math Problem Statement

Solve s^2 - 9 = 0.

Solution

The problem in the image is:

s29=0s^2 - 9 = 0

Step-by-Step Solution:

  1. Isolate s2s^2: s2=9s^2 = 9

  2. Take the square root of both sides: s=±9s = \pm \sqrt{9}

  3. Simplify the square root: s=±3s = \pm 3

Answer:

s=3,3s = 3, -3

Would you like a deeper explanation or have any questions?

Here are five related questions to explore:

  1. How do you solve equations involving higher powers like s39=0s^3 - 9 = 0?
  2. What happens when there is a negative number inside the square root, such as s2+9=0s^2 + 9 = 0?
  3. How can you check if the solutions to s29=0s^2 - 9 = 0 are correct?
  4. What are the properties of the square root function that make ±9\pm \sqrt{9} valid solutions?
  5. How would the solution change if it was s29=ks^2 - 9 = k with kk being a constant?

Tip: Always remember that when you take the square root of a squared term, you must consider both the positive and negative solutions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Square Root
Quadratic Equations

Formulas

s^2 = 9 => s = ±√9

Theorems

Square Root Property

Suitable Grade Level

Grades 8-10