The equation \(x^2 + 6x - 27 = 0\) is a quadratic equation. To solve it, we'll use the quadratic formula:

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

For the equation \(x^2 + 6x - 27 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 6\)
- \(c = -27\)

Substitute these values into the quadratic formula:

\[
x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-27)}}{2(1)}
\]

Simplifying this:

\[
x = \frac{-6 \pm \sqrt{36 + 108}}{2}
\]

\[
x = \frac{-6 \pm \sqrt{144}}{2}
\]

\[
x = \frac{-6 \pm 12}{2}
\]

This gives us two possible solutions:

\[
x_1 = \frac{-6 + 12}{2} = \frac{6}{2} = 3
\]

\[
x_2 = \frac{-6 - 12}{2} = \frac{-18}{2} = -9
\]

So, the solutions to the equation \(x^2 + 6x - 27 = 0\) are:

\[
x = 3 \quad \text{or} \quad x = -9
\]

Would you like further details or have any questions?

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Here are some related questions:

1. How can you verify the solutions of a quadratic equation?
2. What are the steps to solve a quadratic equation by factoring?
3. How does the discriminant determine the nature of the roots?
4. What is the axis of symmetry for a quadratic function?
5. How can you use the quadratic formula to solve equations with complex roots?
6. What is the significance of the vertex in the graph of a quadratic function?
7. How do you solve a quadratic equation by completing the square?
8. What are some practical applications of solving quadratic equations?

**Tip:** Always double-check your calculations, especially when working with square roots, to avoid errors in finding the roots of a quadratic equation.

Learn how to solve the quadratic equation x² + 6× - 27 = 0 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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