solve using the quadratic formula, x^2 +12x + 20 = 0

To solve the quadratic equation \( x^2 + 12x + 20 = 0 \) using the quadratic formula, we follow these steps:

The quadratic formula is:

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

For the given equation \( x^2 + 12x + 20 = 0 \), we can identify the coefficients:
- \( a = 1 \)
- \( b = 12 \)
- \( c = 20 \)

Now, we substitute these values into the quadratic formula:

\[
x = \frac{-12 \pm \sqrt{12^2 - 4(1)(20)}}{2(1)}
\]

Simplify the terms inside the square root:

\[
x = \frac{-12 \pm \sqrt{144 - 80}}{2}
\]

\[
x = \frac{-12 \pm \sqrt{64}}{2}
\]

\[
x = \frac{-12 \pm 8}{2}
\]

Now, solve for the two possible values of \( x \):

1. \( x_1 = \frac{-12 + 8}{2} = \frac{-4}{2} = -2 \)
2. \( x_2 = \frac{-12 - 8}{2} = \frac{-20}{2} = -10 \)

Therefore, the solutions are:

\[
x = -2 \quad \text{or} \quad x = -10
\]

Would you like more details or have any further questions?

Here are 5 related questions to expand on this:
1. How is the discriminant related to the nature of the roots of a quadratic equation?
2. What happens if the discriminant is negative in a quadratic equation?
3. Can you derive the quadratic formula from completing the square method?
4. How would you solve \( x^2 + 12x + 36 = 0 \) using the quadratic formula?
5. What are some real-world applications of quadratic equations?

**Tip:** The discriminant \( \Delta = b^2 - 4ac \) tells you whether the quadratic equation has real or complex roots. If \( \Delta > 0 \), there are two distinct real roots; if \( \Delta = 0 \), there is one real root; if \( \Delta < 0 \), there are two complex roots.

Learn how to solve the quadratic equation x^2 + 12x + 20 using the quadratic formula. This step-by-step solution covers algebraic concepts and the quadratic formula, making it perfect for students in Grades 8-10.

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