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The question asks for the discriminant of the quadratic equation \(x^2 + 4x = 5\). Let’s solve it step by step.

### Step 1: Rewrite the equation in standard quadratic form
The standard quadratic form is:
\[
ax^2 + bx + c = 0
\]
Given:
\[
x^2 + 4x = 5
\]
Rewrite it as:
\[
x^2 + 4x - 5 = 0
\]
So, \(a = 1\), \(b = 4\), and \(c = -5\).

### Step 2: Formula for the discriminant
The discriminant \(D\) of a quadratic equation is given by:
\[
D = b^2 - 4ac
\]

### Step 3: Substituting the values
\[
D = 4^2 - 4(1)(-5)
\]
\[
D = 16 + 20 = 36
\]

### Step 4: Correct answer
The discriminant value is:
\[
D = 36
\]

Thus, the correct answer is **36**.

Would you like a deeper explanation of discriminants or quadratic equations?

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Here are 5 related questions for further exploration:
1. How do we determine the number of roots from the discriminant?
2. What happens if the discriminant is negative, zero, or positive?
3. How do you factor a quadratic equation if the discriminant is a perfect square?
4. What are the real roots of this equation \(x^2 + 4x - 5 = 0\)?
5. Can you solve a quadratic equation with a discriminant of zero?

**Tip:** If the discriminant is positive, the equation has two distinct real roots!

Apskaičiuokite kvadratinės lygties x^2 + 4x = 5 diskriminanto reikšmę. Pažymėkite teisingą atsakymą.

Learn how to calculate the discriminant of the quadratic equation x^2 + 4x = 5. This step-by-step solution walks through the use of the discriminant formula D = b^2 - 4ac, helping students in Grades 8-10 grasp key concepts in algebra.

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