The given expression is \( 2x^2 - 12x + 7 \).

To solve or simplify it, there are a few things we can do depending on what you're looking for:

### 1. **Factoring (if possible):**
We can attempt to factor this quadratic expression. However, this quadratic does not factor nicely using integers. 

### 2. **Quadratic Formula:**
We can use the quadratic formula to find the roots of the equation \( 2x^2 - 12x + 7 = 0 \). The quadratic formula is:

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

For the equation \( 2x^2 - 12x + 7 = 0 \), the coefficients are:
- \( a = 2 \)
- \( b = -12 \)
- \( c = 7 \)

Plugging these values into the quadratic formula:

\[
x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4(2)(7)}}{2(2)}
\]
\[
x = \frac{12 \pm \sqrt{144 - 56}}{4}
\]
\[
x = \frac{12 \pm \sqrt{88}}{4}
\]
\[
x = \frac{12 \pm 2\sqrt{22}}{4}
\]
\[
x = \frac{6 \pm \sqrt{22}}{2}
\]

Thus, the solutions are:

\[
x = \frac{6 + \sqrt{22}}{2} \quad \text{or} \quad x = \frac{6 - \sqrt{22}}{2}
\]

These are the two roots of the quadratic equation.

Would you like more details on any specific part of this solution?

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Here are five related questions:
1. What is the discriminant of a quadratic equation, and how does it determine the nature of the roots?
2. How do we simplify expressions involving square roots, like \( \sqrt{88} \)?
3. How can we complete the square for the quadratic \( 2x^2 - 12x + 7 \)?
4. How do we graph the quadratic function \( 2x^2 - 12x + 7 \)?
5. What is the axis of symmetry for a quadratic function?

**Tip:** Always check the discriminant before factoring or using the quadratic formula—it gives insight into the number and type of solutions!

Explore how to solve the quadratic equation 2x^2 - 12x + 7 using the quadratic formula. This solution includes detailed steps, from identifying coefficients to calculating the discriminant and finding the roots. Suitable for students in Grades 9-11.

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