The equation you provided is:

\[
x^2 + x = 4
\]

To solve for \(x\), follow these steps:

1. Rearrange the equation to set it equal to zero:
   \[
   x^2 + x - 4 = 0
   \]

   This is a quadratic equation of the form \(ax^2 + bx + c = 0\), where \(a = 1\), \(b = 1\), and \(c = -4\).

2. Use the quadratic formula to solve for \(x\):
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   Substituting the values of \(a\), \(b\), and \(c\) into the formula:
   \[
   x = \frac{-1 \pm \sqrt{1^2 - 4(1)(-4)}}{2(1)}
   \]
   Simplify:
   \[
   x = \frac{-1 \pm \sqrt{1 + 16}}{2}
   \]
   \[
   x = \frac{-1 \pm \sqrt{17}}{2}
   \]
   Therefore, the solutions are:
   \[
   x = \frac{-1 + \sqrt{17}}{2} \quad \text{or} \quad x = \frac{-1 - \sqrt{17}}{2}
   \]

These are the two possible solutions for \(x\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you complete the square to solve quadratic equations?
2. What are the steps to solve a quadratic equation using factoring?
3. How is the discriminant in the quadratic formula interpreted?
4. How do you graph the equation \(x^2 + x - 4 = 0\)?
5. What real-life situations can quadratic equations model?

**Tip:** The discriminant \(b^2 - 4ac\) in the quadratic formula tells you how many real solutions the equation has: if it's positive, there are two real solutions.

Learn how to solve the quadratic equation x^2 + x = 4 by using the quadratic formula. This step-by-step solution explains core algebraic concepts, key formulas, and the quadratic formula theorem. Ideal for students in Grades 9-10.

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