Solve the equation by completing the square.

xsquared2minus−1313xplus+3636equals=0

To solve the quadratic equation \( x^2 - 13x + 36 = 0 \) by completing the square, follow these steps:

### 1. Move the constant term to the right-hand side
First, subtract 36 from both sides:
\[
x^2 - 13x = -36
\]

### 2. Complete the square
Take half of the coefficient of \(x\), which is \(-13\), divide by 2, and then square it:
\[
\left(\frac{-13}{2}\right)^2 = \left(\frac{-13}{2}\right)^2 = \frac{169}{4}
\]
Now, add this value to both sides of the equation:
\[
x^2 - 13x + \frac{169}{4} = -36 + \frac{169}{4}
\]

### 3. Simplify the right-hand side
Convert \(-36\) to a fraction with the same denominator:
\[
-36 = \frac{-144}{4}
\]
Now, simplify the right-hand side:
\[
-36 + \frac{169}{4} = \frac{-144 + 169}{4} = \frac{25}{4}
\]

### 4. Write the left-hand side as a perfect square
The left-hand side is now a perfect square:
\[
\left(x - \frac{13}{2}\right)^2 = \frac{25}{4}
\]

### 5. Take the square root of both sides
Take the square root of both sides of the equation:
\[
x - \frac{13}{2} = \pm \frac{5}{2}
\]

### 6. Solve for \(x\)
Now solve for \(x\) by adding \(\frac{13}{2}\) to both sides:
\[
x = \frac{13}{2} \pm \frac{5}{2}
\]
This gives two solutions:
\[
x = \frac{13 + 5}{2} = 9 \quad \text{or} \quad x = \frac{13 - 5}{2} = 4
\]

### Final Solution:
The solutions are:
\[
x = 9 \quad \text{or} \quad x = 4
\]

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

Here are 5 related questions to further your understanding:
1. Can you complete the square for the equation \(x^2 + 6x + 5 = 0\)?
2. How does the method of completing the square relate to the quadratic formula?
3. Can you solve \(x^2 - 8x + 12 = 0\) using a different method?
4. What happens when the quadratic equation has no real solutions?
5. Can you explain how to find the vertex of a parabola using completing the square?

**Tip:** Completing the square is a great method not just for solving equations but also for transforming equations into vertex form for graphing parabolas.

Solve the equation by completing the square: x^2 - 13x + 36 = 0

Learn how to solve the quadratic equation x^2 - 13x + 36 = 0 using the method of completing the square. This detailed step-by-step solution demonstrates key algebraic concepts and is suitable for students in Grades 8-10. Discover related questions and practice problems to deepen your understanding.

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