Quadratic equation by completing square X² - 2x +3 = 0


To solve the quadratic equation \(x^2 - 2x + 3 = 0\) by completing the square, follow these steps:

1. **Rewrite the equation**:  
   Start with the given equation:  
   \[
   x^2 - 2x + 3 = 0
   \]

2. **Move the constant term to the other side**:  
   Subtract 3 from both sides:
   \[
   x^2 - 2x = -3
   \]

3. **Complete the square**:  
   To complete the square, take half of the coefficient of \(x\) (which is \(-2\)), square it, and add it to both sides:
   \[
   \left(\frac{-2}{2}\right)^2 = 1
   \]
   Add 1 to both sides:
   \[
   x^2 - 2x + 1 = -3 + 1
   \]
   \[
   (x - 1)^2 = -2
   \]

4. **Solve for \(x\)**:  
   Now, take the square root of both sides:
   \[
   x - 1 = \pm \sqrt{-2}
   \]
   Since \(\sqrt{-2} = i\sqrt{2}\), where \(i\) is the imaginary unit, we get:
   \[
   x - 1 = \pm i\sqrt{2}
   \]
   Solve for \(x\) by adding 1 to both sides:
   \[
   x = 1 \pm i\sqrt{2}
   \]

Thus, the solutions are:
\[
x = 1 + i\sqrt{2} \quad \text{or} \quad x = 1 - i\sqrt{2}
\]

Would you like more details on any step or have any questions?

Here are 5 related questions you might explore:
1. How do you solve quadratic equations using the quadratic formula?
2. What is the discriminant of a quadratic equation, and what does it tell us?
3. Can all quadratic equations be solved by completing the square?
4. How do you perform arithmetic with complex numbers like \(1 \pm i\sqrt{2}\)?
5. What is the geometric interpretation of the roots of a quadratic equation?

**Tip**: Completing the square is also useful for converting quadratic equations into vertex form, which makes it easier to graph.

Quadratic equation by completing square X² - 2x + 3 = 0

Learn how to solve the quadratic equation x² - 2x + 3 = 0 by completing the square. This step-by-step guide covers key algebraic techniques, including completing the square and dealing with complex numbers, suitable for students in Grades 9-11.

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