https://file.aiquickdraw.com/mathbot/file/1725484591193xupz19bo.jpg

The equation in the image is:

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

This is a quadratic equation. To solve it, we can follow these steps:

### Step 1: Rearrange the equation
Move all terms to one side to set the equation to 0:

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

### Step 2: Apply the quadratic formula
The quadratic formula is given by:

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

For the equation \(x^2 + 7x - 4 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 7\)
- \(c = -4\)

### Step 3: Calculate the discriminant
\[
\Delta = b^2 - 4ac = 7^2 - 4(1)(-4) = 49 + 16 = 65
\]

### Step 4: Solve for \(x\)
Now substitute the values into the quadratic formula:

\[
x = \frac{-7 \pm \sqrt{65}}{2(1)} = \frac{-7 \pm \sqrt{65}}{2}
\]

Thus, the solutions are:

\[
x_1 = \frac{-7 + \sqrt{65}}{2}, \quad x_2 = \frac{-7 - \sqrt{65}}{2}
\]

These are the exact solutions. If you prefer approximate decimal values:

\[
x_1 \approx \frac{-7 + 8.06}{2} \approx 0.53, \quad x_2 \approx \frac{-7 - 8.06}{2} \approx -7.53
\]

Would you like more details on any of these steps or a further explanation?

Here are 5 related questions you might want to explore:
1. How does the discriminant affect the nature of the solutions?
2. What are other methods for solving quadratic equations?
3. Can this quadratic equation be factored directly?
4. How would this problem change if the right-hand side was a different number?
5. What are complex solutions in quadratic equations, and when do they occur?

**Tip**: Always double-check your discriminant calculation to ensure you're solving the quadratic equation correctly.

Learn how to solve the quadratic equation x^2 + 7x = 4 using the quadratic formula. This solution covers key algebraic concepts and provides step-by-step instructions. Ideal for students in Grades 7-9.

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