To solve the quadratic equation \(x^2 + 10x - 11 = 0\), we can use the **quadratic formula**:

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

For the equation \(x^2 + 10x - 11 = 0\), the coefficients are:

- \(a = 1\)
- \(b = 10\)
- \(c = -11\)

### Step 1: Apply the values into the formula
\[
x = \frac{-10 \pm \sqrt{10^2 - 4(1)(-11)}}{2(1)}
\]

### Step 2: Simplify under the square root
\[
x = \frac{-10 \pm \sqrt{100 + 44}}{2}
\]
\[
x = \frac{-10 \pm \sqrt{144}}{2}
\]

### Step 3: Take the square root of 144
\[
x = \frac{-10 \pm 12}{2}
\]

### Step 4: Solve for the two possible values of \(x\)
\[
x_1 = \frac{-10 + 12}{2} = \frac{2}{2} = 1
\]
\[
x_2 = \frac{-10 - 12}{2} = \frac{-22}{2} = -11
\]

### Final Answer:
The solutions are:
\[
x = 1 \quad \text{or} \quad x = -11
\]

Would you like further clarification or details?

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Here are 5 related questions for practice:
1. Solve \(x^2 - 7x + 12 = 0\).
2. What are the solutions to the equation \(2x^2 - 5x + 3 = 0\)?
3. Factor the quadratic equation \(x^2 + 6x + 9 = 0\).
4. How do you solve \(x^2 + 12x + 36 = 0\) using the quadratic formula?
5. Find the roots of \(3x^2 - x - 4 = 0\).

**Tip**: When using the quadratic formula, always check the discriminant \((b^2 - 4ac)\) to determine if the roots are real, complex, or repeated.

Learn how to solve the quadratic equation x² + 10x - 11 = 0 using the quadratic formula. This step-by-step guide simplifies the process and covers essential algebraic concepts. Perfect for Grades 7-9 students.

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