Let's solve the quadratic equation:

\[
x^2 - 13x = -30
\]

### Step 1: Move all terms to one side of the equation

Add \(30\) to both sides of the equation to get:

\[
x^2 - 13x + 30 = 0
\]

### Step 2: Solve using the quadratic formula

The quadratic formula is given by:

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

For the equation \(x^2 - 13x + 30 = 0\), the coefficients are:
- \(a = 1\)
- \(b = -13\)
- \(c = 30\)

Substituting these values into the quadratic formula:

\[
x = \frac{-(-13) \pm \sqrt{(-13)^2 - 4(1)(30)}}{2(1)}
\]

Simplify step by step:

\[
x = \frac{13 \pm \sqrt{169 - 120}}{2}
\]

\[
x = \frac{13 \pm \sqrt{49}}{2}
\]

\[
x = \frac{13 \pm 7}{2}
\]

### Step 3: Find the two possible values for \(x\)

1. \(x = \frac{13 + 7}{2} = \frac{20}{2} = 10\)
2. \(x = \frac{13 - 7}{2} = \frac{6}{2} = 3\)

### Final Answer:

The solutions are:

\[
x = 10 \quad \text{or} \quad x = 3
\]

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. How can you factor the quadratic equation \(x^2 - 13x + 30 = 0\)?
2. How does the quadratic formula work for equations with imaginary roots?
3. What is the axis of symmetry for the parabola represented by the equation \(y = x^2 - 13x + 30\)?
4. Can you find the vertex of the parabola described by \(y = x^2 - 13x + 30\)?
5. How would you solve the equation \(x^2 - 13x + 30 = 0\) by completing the square?

**Tip:** When solving quadratic equations, if the quadratic can be factored easily, factoring can be quicker than using the quadratic formula.

Learn how to solve the quadratic equation x^2 - 13x = -30 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic formula. Suitable for students in Grades 7-9.

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