Solve for x in the equation x squared + 20 x + 100 = 36.
x = –16 or x = –4
x = –10
x = –8
x = 4 or x = 16

We are given the equation:

\[
x^2 + 20x + 100 = 36
\]

### Step 1: Move 36 to the left side by subtracting 36 from both sides:
\[
x^2 + 20x + 100 - 36 = 0
\]
\[
x^2 + 20x + 64 = 0
\]

### Step 2: Factor the quadratic equation.
We look for two numbers that multiply to give 64 and add to give 20. These numbers are 8 and 8. So we can factor the quadratic as:
\[
(x + 8)(x + 8) = 0
\]
This simplifies to:
\[
(x + 8)^2 = 0
\]

### Step 3: Solve for \(x\).
\[
x + 8 = 0
\]
\[
x = -8
\]

Thus, the solution is \(x = -8\).

### Answer:
The correct solution is:
\[
x = -8
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you factor a quadratic equation?
2. What is the discriminant, and how is it used in solving quadratic equations?
3. Can a quadratic equation have no real solutions?
4. How do you complete the square to solve a quadratic equation?
5. What are the applications of quadratic equations in real life?

**Tip:** Always check if a quadratic equation can be factored before using more complex methods like completing the square or the quadratic formula.

Solve for x in the equation x squared + 20 x + 100 = 36.

This tutorial explains how to solve the quadratic equation x^2 + 20x + 100 = 36 by factoring. Learn key algebraic concepts, including factoring, the quadratic equation formula, and using the zero product property. Suitable for students in Grades 8-10.

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