To solve the equation \(x^2 = 12\), follow these steps:

### Step 1: Simplify the Equation
The equation is already in a simple form: \(x^2 = 12\).

### Step 2: Take the Square Root of Both Sides
To solve for \(x\), take the square root of both sides:
\[
x = \pm \sqrt{12}
\]

### Step 3: Simplify the Square Root
\(\sqrt{12}\) can be simplified further:
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]

### Final Answer
The solutions to the equation are:
\[
x = \pm 2\sqrt{3}
\]

So, \(x = 2\sqrt{3}\) or \(x = -2\sqrt{3}\).

Would you like more details or have any questions?

Here are some related questions:
1. How do you solve \(x^2 = 20\)?
2. What are the properties of square roots?
3. How can you solve a quadratic equation like \(x^2 + 3x - 4 = 0\)?
4. What happens if the equation is \(x^2 = -12\)?
5. How can you rationalize the denominator when dealing with square roots?

**Tip:** Simplifying square roots by breaking them into factors can make solving equations easier.

Learn how to solve the equation x^2 = 12 using the square root method with a detailed step-by-step solution. This problem covers key algebraic concepts, including quadratic equations and square root simplification. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation