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To solve the quadratic equation by factoring, we first need to rewrite it in standard form. 

The given equation is:
\[
x^2 = 3x + 4
\]

### Step 1: Move all terms to one side of the equation.
\[
x^2 - 3x - 4 = 0
\]

### Step 2: Factor the quadratic.
We are looking for two numbers that multiply to \(-4\) (the constant term) and add up to \(-3\) (the coefficient of \(x\)).

The numbers \(-4\) and \(1\) satisfy this condition:
\[
-4 \times 1 = -4 \quad \text{and} \quad -4 + 1 = -3
\]

So, we can factor the quadratic as:
\[
(x - 4)(x + 1) = 0
\]

### Step 3: Solve for \(x\).
Using the zero product property, set each factor equal to zero:
\[
x - 4 = 0 \quad \text{or} \quad x + 1 = 0
\]

Solving these gives:
\[
x = 4 \quad \text{or} \quad x = -1
\]

### Final Answer:
The solutions to the equation are:
\[
x = 4 \quad \text{or} \quad x = -1
\]

Would you like more details on any part of this solution, or have any other questions?

Here are 5 related questions to further expand on this:
1. How can we verify the solutions of a factored quadratic equation?
2. What are some alternative methods to solve quadratic equations?
3. Can every quadratic equation be solved by factoring?
4. What is the discriminant, and how does it help in solving quadratic equations?
5. How do the solutions change if the quadratic equation has no real roots?

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

Solve the quadratic by factoring: x^2 = 3x + 4

Learn how to solve the quadratic equation x^2 = 3x + 4 by factoring. This problem covers essential algebraic concepts like factoring quadratics and applying the zero-product property. Suitable for students in Grades 8-10.

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