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 using the quadratic formula, let's start with the given equation:

\[
x^2 - 6x + 2 = 0
\]

The quadratic formula is:

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

In this equation, we have:
- \( a = 1 \)
- \( b = -6 \)
- \( c = 2 \)

### Step 1: Plug the values of \(a\), \(b\), and \(c\) into the quadratic formula.

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

### Step 2: Simplify inside the square root.

\[
x = \frac{6 \pm \sqrt{36 - 8}}{2}
\]

\[
x = \frac{6 \pm \sqrt{28}}{2}
\]

### Step 3: Simplify the square root.

\[
\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}
\]

So, the equation becomes:

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

### Step 4: Simplify the expression by dividing both terms in the numerator by 2.

\[
x = 3 \pm \sqrt{7}
\]

Thus, the two solutions are:

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

### Final Answer:

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

Make sure to enter your answers as:

\[
(3-\sqrt{7}), (3+\sqrt{7})
\]

---

Do you have any questions or need more details on any step? 

Here are 5 related questions:
1. How do you derive the discriminant of a quadratic equation?
2. What happens if the discriminant is negative?
3. Can the quadratic formula always be used to solve quadratic equations?
4. What are some alternative methods to solve quadratic equations besides using the quadratic formula?
5. How can we factor a quadratic equation when the roots are rational numbers?

**Tip:** Always simplify square roots where possible before using the quadratic formula to make calculations easier!

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

Learn how to solve the quadratic equation x^2 - 6x + 2 using the quadratic formula. This step-by-step guide covers algebraic concepts and demonstrates how to simplify square roots, perfect for Grades 9-10 students.

Math Problem Statement

x 2 − 6 x + 2

For example, if
x

x

Solution

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