To solve the equation $x^2 - 10x + 4 = 0$ by completing the square, let's go through the steps:

Step 1: Move the constant term to the other side.

First, rewrite the equation to make it easier to complete the square: $x^2 - 10x = -4$

Step 2: Complete the square.

To complete the square, we need to add and subtract the square of half the coefficient of $x$. The coefficient of $x$ is $-10$, so half of $-10$ is $-5$, and $(-5)^2 = 25$.

Add 25 to both sides of the equation: $x^2 - 10x + 25 = -4 + 25$ $(x - 5)^2 = 21$

Step 3: Solve for $x$.

Now, take the square root of both sides: $x - 5 = \pm \sqrt{21}$

Finally, solve for $x$ by adding 5 to both sides: $x = 5 \pm \sqrt{21}$

So the two solutions are: $x = 5 + \sqrt{21} \quad \text{or} \quad x = 5 - \sqrt{21}$

Would you like more details on any of the steps, or do you have any questions?

Related Questions:

1. How do you know when to complete the square versus using the quadratic formula?
2. What is the significance of completing the square in solving quadratic equations?
3. How would the method change if the coefficient of $x^2$ were not 1?
4. How can you use the solutions found to factor the original quadratic equation?
5. What are the real-world applications of solving quadratic equations?

Tip:

When completing the square, always remember to balance the equation by adding the same value to both sides!