Solve for x in the equation x squared + 10 x + 12 = 36.

To solve for \( x \) in the equation:

\[
x^2 + 10x + 12 = 36
\]

### Step 1: Simplify the equation

Subtract 36 from both sides to set the equation to 0:

\[
x^2 + 10x + 12 - 36 = 0
\]
\[
x^2 + 10x - 24 = 0
\]

### Step 2: Factor the quadratic equation

Now, we need to factor the quadratic expression \( x^2 + 10x - 24 = 0 \).

We are looking for two numbers that multiply to give -24 and add up to 10. These numbers are 12 and -2.

\[
x^2 + 12x - 2x - 24 = 0
\]

Group the terms:

\[
(x^2 + 12x) - (2x + 24) = 0
\]

Factor out the common factors:

\[
x(x + 12) - 2(x + 12) = 0
\]

Now factor out \( (x + 12) \):

\[
(x - 2)(x + 12) = 0
\]

### Step 3: Solve for \( x \)

Now that we have factored the equation, set each factor to 0:

1. \( x - 2 = 0 \Rightarrow x = 2 \)
2. \( x + 12 = 0 \Rightarrow x = -12 \)

### Final Solution:
The solutions are \( x = 2 \) and \( x = -12 \).

Would you like more details on factoring or quadratic equations?

Here are some related questions you might be interested in:
1. How can I solve quadratic equations using the quadratic formula?
2. What is the difference between factoring and completing the square?
3. How can I solve quadratic equations graphically?
4. What are the applications of quadratic equations in real life?
5. How do I recognize when a quadratic equation cannot be factored easily?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they are correct.

Solve for x in the equation x squared + 10x + 12 = 36.

Learn how to solve the quadratic equation x^2 + 10x - 24 = 0 using factoring methods. This detailed solution walks through simplifying the equation, factoring, and applying the zero product property. Suitable for students in Grades 8-10.

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