To solve the quadratic equation by completing the square, we start with:

$x^2 - 4x - 60 = 0$

Step 1: Move the constant term to the other side

Add $60$ to both sides to get: $x^2 - 4x = 60$

Step 2: Complete the square

1. Take half of the coefficient of $x$, which is $-4$. Half of $-4$ is $-2$.
2. Square $-2$ to get $4$, then add $4$ to both sides:

$x^2 - 4x + 4 = 60 + 4$

This simplifies to: $(x - 2)^2 = 64$

Step 3: Take the square root of both sides

$x - 2 = \pm \sqrt{64}$ $x - 2 = \pm 8$

Step 4: Solve for $x$

1. For $x - 2 = 8$:
   $x = 8 + 2 = 10$

2. For $x - 2 = -8$:
   $x = -8 + 2 = -6$

Solution

The solutions are: $x = 10 \quad \text{and} \quad x = -6$

Would you like further clarification or have any questions?

---

Related Questions

1. How do you complete the square for a quadratic equation with a leading coefficient other than 1?
2. What are alternative methods to solve a quadratic equation?
3. How does completing the square relate to the quadratic formula?
4. What is the significance of the vertex form of a quadratic equation?
5. How can completing the square be used to find the minimum or maximum value of a quadratic function?

Tip

When completing the square, always make sure to balance the equation by adding the same value to both sides.