https://file.aiquickdraw.com/mathbot/file/17254157511167fuji3wy.jpg

The equation in the image is:

\[ 4x^2 + 7x - 8 = -8x - 4 \]

To solve this equation, follow these steps:

1. **Move all terms to one side**: 
   To do this, add \(8x\) and \(4\) to both sides.

   \[
   4x^2 + 7x + 8x - 8 + 4 = 0
   \]

   Simplifying:

   \[
   4x^2 + 15x - 4 = 0
   \]

2. **Solve the quadratic equation**:
   We can solve the quadratic equation using the quadratic formula:

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

   Here, \(a = 4\), \(b = 15\), and \(c = -4\).

   First, calculate the discriminant:

   \[
   \text{Discriminant} = b^2 - 4ac = 15^2 - 4(4)(-4) = 225 + 64 = 289
   \]

   Since the discriminant is positive, we will have two real roots.

   Now, substitute the values into the quadratic formula:

   \[
   x = \frac{-15 \pm \sqrt{289}}{8} = \frac{-15 \pm 17}{8}
   \]

   This gives us two solutions:

   \[
   x_1 = \frac{-15 + 17}{8} = \frac{2}{8} = \frac{1}{4}
   \]

   \[
   x_2 = \frac{-15 - 17}{8} = \frac{-32}{8} = -4
   \]

So, the solutions to the equation are \( x = \frac{1}{4} \) and \( x = -4 \).

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What happens if the discriminant in the quadratic formula is negative?
2. How do you derive the quadratic formula?
3. Can you solve this quadratic equation by factoring?
4. What is the significance of the discriminant in determining the nature of the roots?
5. How can you verify the solutions of a quadratic equation by substitution?

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

Solve the quadratic equation: 4x^2 + 7x - 8 = -8x - 4.

Learn how to solve the quadratic equation 4x^2 + 7x - 8 = -8x - 4 with detailed steps. This problem involves algebraic concepts such as the quadratic formula and discriminant, and is suitable for students in Grades 8-10.

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