slove using the quadtraic equation x^2+4x-12=0

To solve the quadratic equation \( x^2 + 4x - 12 = 0 \) using the quadratic formula, we can follow these steps:

The quadratic formula is:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
where \(a\), \(b\), and \(c\) are the coefficients from the general quadratic equation \(ax^2 + bx + c = 0\).

For the equation \(x^2 + 4x - 12 = 0\):
- \(a = 1\)
- \(b = 4\)
- \(c = -12\)

Now, plug these values into the quadratic formula:

\[
x = \frac{-4 \pm \sqrt{4^2 - 4(1)(-12)}}{2(1)}
\]
Simplify inside the square root:
\[
x = \frac{-4 \pm \sqrt{16 + 48}}{2}
\]
\[
x = \frac{-4 \pm \sqrt{64}}{2}
\]
\[
x = \frac{-4 \pm 8}{2}
\]

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

1. \( x_1 = \frac{-4 + 8}{2} = \frac{4}{2} = 2 \)
2. \( x_2 = \frac{-4 - 8}{2} = \frac{-12}{2} = -6 \)

Thus, the solutions are:
\[
x = 2 \quad \text{or} \quad x = -6
\]

Would you like a detailed explanation of any step or have any questions?

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Here are 5 related questions:
1. How can you factor a quadratic equation instead of using the quadratic formula?
2. What are the key differences between real and complex solutions in quadratics?
3. How does the discriminant \(b^2 - 4ac\) affect the nature of the solutions?
4. Can every quadratic equation be solved using the quadratic formula?
5. What are the geometric interpretations of quadratic solutions on a graph?

**Tip:** Always check the discriminant first to determine if the solutions will be real or complex!

slove using the quadratic equation x^2+4x-12=0

Learn how to solve the quadratic equation x^2 + 4x - 12 using the quadratic formula. This step-by-step solution explores key algebraic concepts such as the quadratic formula and discriminant, ideal for students in Grades 7-9.

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