Math Problem Statement

X²=12

Solution

To solve the equation x2=12x^2 = 12, follow these steps:

Step 1: Simplify the Equation

The equation is already in a simple form: x2=12x^2 = 12.

Step 2: Take the Square Root of Both Sides

To solve for xx, take the square root of both sides: x=±12x = \pm \sqrt{12}

Step 3: Simplify the Square Root

12\sqrt{12} can be simplified further: 12=4×3=4×3=23\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}

Final Answer

The solutions to the equation are: x=±23x = \pm 2\sqrt{3}

So, x=23x = 2\sqrt{3} or x=23x = -2\sqrt{3}.

Would you like more details or have any questions?

Here are some related questions:

  1. How do you solve x2=20x^2 = 20?
  2. What are the properties of square roots?
  3. How can you solve a quadratic equation like x2+3x4=0x^2 + 3x - 4 = 0?
  4. What happens if the equation is x2=12x^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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Square Roots

Formulas

Quadratic equation formula ax^2 + bx + c = 0
Square root simplification

Theorems

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Suitable Grade Level

Grades 9-12