To solve the equation:

\[
3x^2 - 20x - 400 = 0
\]

we can use the quadratic formula, which is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

where \( a = 3 \), \( b = -20 \), and \( c = -400 \).

### Step 1: Plug values into the formula
1. **Calculate \( b^2 - 4ac \):**
   \[
   (-20)^2 - 4 \cdot 3 \cdot (-400) = 400 + 4800 = 5200
   \]

2. **Take the square root of 5200:**
   \[
   \sqrt{5200} = 20\sqrt{13}
   \]

3. **Solve for \( x \):**
   \[
   x = \frac{20 \pm 20\sqrt{13}}{6} = \frac{10 \pm 10\sqrt{13}}{3}
   \]

### Solutions:
\[
x = \frac{10 + 10\sqrt{13}}{3} \quad \text{and} \quad x = \frac{10 - 10\sqrt{13}}{3}
\]

Let me know if you need further details, and here are some related questions for practice:

1. How do you simplify the square root of large numbers?
2. What are the steps to derive the quadratic formula?
3. How can you verify solutions to a quadratic equation?
4. What if a quadratic equation has no real roots?
5. How do coefficients affect the shape of a parabola?

**Tip:** Always simplify square roots when possible for cleaner answers.

Learn to solve the quadratic equation 3x^2 - 20x - 400 = 0 using the quadratic formula. This step-by-step solution explains key algebraic concepts and calculations, including finding square roots and simplifying. Ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation