Solve equation by factoring: x squared-16x+64=0

To solve the quadratic equation by factoring, we have:

\[
x^2 - 16x + 64 = 0
\]

### Step 1: Identify the coefficients
The equation is already in standard form \(ax^2 + bx + c = 0\), where:
- \(a = 1\)
- \(b = -16\)
- \(c = 64\)

### Step 2: Factor the quadratic expression
We need to find two numbers that multiply to \(c = 64\) and add up to \(b = -16\).

The factors of 64 that add up to -16 are -8 and -8. So, we can factor the quadratic as:

\[
x^2 - 16x + 64 = (x - 8)(x - 8) = (x - 8)^2
\]

### Step 3: Set each factor equal to zero
Since \((x - 8)^2 = 0\), we have:

\[
x - 8 = 0
\]

### Step 4: Solve for \(x\)
\[
x = 8
\]

### Final Answer
The solution to the equation is:

\[
x = 8
\]

Would you like more details on this solution, or do you have any questions?

### Related Questions:
1. How do you solve a quadratic equation by completing the square?
2. What are the methods to solve quadratic equations other than factoring?
3. Can a quadratic equation have two distinct real roots?
4. What is the quadratic formula, and when is it used?
5. How can you determine the nature of the roots of a quadratic equation?

### Tip:
Always check if a quadratic expression can be factored easily before using more complex methods like the quadratic formula. Factoring is often the quickest method!

Solve equation by factoring: x squared - 16x + 64 = 0

Learn how to solve the quadratic equation x^2 - 16x + 64 by factoring. This step-by-step guide covers key algebraic concepts, including factoring and the quadratic equation formula. Perfect for students in Grades 7-9 looking to master factoring methods.

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