Use the quadratic formula to solve the equation. Be sure to simplify your answers. Enter both answers separated by a comma.

x
2
−
6
x
+
2
=
0

For example, if
x
=
−
5
±
√
15
4
you enter

(-5-sqrt(15))/4 on the left and (-5+sqrt(15))/4 on the right.

Note the important placement of parentheses! Use the PREVIEW button!

x
=

To solve the quadratic equation \( x^2 - 6x + 2 = 0 \) using the quadratic formula:

The quadratic formula is given by:

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

Here, \( a = 1 \), \( b = -6 \), and \( c = 2 \).

### Step 1: Calculate the discriminant
The discriminant \( \Delta \) is:

\[
\Delta = b^2 - 4ac = (-6)^2 - 4(1)(2) = 36 - 8 = 28
\]

### Step 2: Apply the quadratic formula
Now, plug the values into the quadratic formula:

\[
x = \frac{-(-6) \pm \sqrt{28}}{2(1)} = \frac{6 \pm \sqrt{28}}{2}
\]

### Step 3: Simplify the square root of 28
\[
\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}
\]

So, the expression becomes:

\[
x = \frac{6 \pm 2\sqrt{7}}{2}
\]

### Step 4: Simplify further
\[
x = \frac{6}{2} \pm \frac{2\sqrt{7}}{2} = 3 \pm \sqrt{7}
\]

Thus, the two solutions are:

\[
x = 3 - \sqrt{7}, \quad x = 3 + \sqrt{7}
\]

### Final Answer:
In the required format:

\[
x = \frac{(3-\sqrt{7})}{1}, \quad x = \frac{(3+\sqrt{7})}{1}
\]

Let me know if you'd like any more details or have any questions!

---

Here are 5 related questions to expand on the concept:

1. How do you determine the number of real solutions using the discriminant?
2. How does the quadratic formula change if the discriminant is negative?
3. Can the quadratic formula be used to solve all types of quadratic equations?
4. How would the quadratic formula change if the coefficient of \(x^2\) was not 1?
5. How does the quadratic formula relate to completing the square?

**Tip**: Always check the discriminant first, as it tells you if your solutions will be real, complex, or repeated.

Use the quadratic formula to solve the equation. Be sure to simplify your answers. Enter both answers separated by a comma. x^2 - 6x + 2 = 0

Step-by-step solution to solve the quadratic equation x^2 - 6x + 2 using the quadratic formula. Learn how to calculate the discriminant, simplify the square root, and find the two roots of the equation. Suitable for Grades 8-10.

Math Problem Statement

x 2 − 6 x + 2

For example, if x

x

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