solve the equation for x using the quadratic formula:

3x^2 + 8x + 1 = 0

Work:

I tried factoring it, but I can't do it.

(3x + ?)(x + ?)
I'm thinking the ? = 1 but that won't work.

The problem says to solve it using the quadratic formula? Why are you trying to factor it?

Ahh wait I got it. I was thinking something weird. I jus thave to plug it in

3x^2-8x+1=0

To solve the quadratic equation 3x^2 + 8x + 1 = 0 using the quadratic formula, you can follow these steps:

Step 1: Identify the coefficients of the equation. In this case, the coefficient of x^2 is 3, the coefficient of x is 8, and the constant term is 1.

Step 2: Write down the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

In this formula, a represents the coefficient of x^2, b represents the coefficient of x, and c represents the constant term.

Step 3: Substitute the coefficients into the quadratic formula:
x = (-8 ± √(8^2 - 4 * 3 * 1)) / (2 * 3)

Step 4: Simplify the equation inside the square root:
x = (-8 ± √(64 - 12)) / 6
x = (-8 ± √(52)) / 6

Step 5: Further simplify the equation under the square root:
x = (-8 ± √(4 * 13)) / 6
x = (-8 ± 2√13) / 6

Step 6: Divide the numerator and denominator by the greatest common factor, 2:
x = (-4 ± √13) / 3

So, the solutions for the equation 3x^2 + 8x + 1 = 0 using the quadratic formula are:
x = (-4 + √13) / 3
x = (-4 - √13) / 3