Solve the equation for all values of x by completing the square.
x, squared, minus, 4, x, minus, 60, equals, 0
x 
2
 −4x−60=
0

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?

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### 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.

Solve the equation for all values of x by completing the square. x^2 − 4x − 60 = 0

Learn how to solve the quadratic equation x^2 - 4x - 60 = 0 using the method of completing the square. This step-by-step solution guides students through isolating terms, balancing the equation, and finding the roots of the quadratic equation. Perfect for students in Grades 8-10 studying algebraic methods.

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