3x^2-12x+11=0

Solve for x.

Ummmmmmmm. How is that easy??????????

It's only easy if you know the quadratic formula:

x = [12 ± √(144-132)]/6
= (12 ± √12)/6
= 2 ± √3/3
= 1.423 or 2.577

Answer in the book is 6±√3/3

I was able to get to (12 ± √12)/6 but I couldn't figure out how you got the rest.

4x+y=12

6x+8y=8

12. 🎓 🎥💽📼

To solve the quadratic equation 3x^2 - 12x + 11 = 0, you can use the quadratic formula.

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where the equation is in the form ax^2 + bx + c = 0.

In this case, a = 3, b = -12, and c = 11.

Substitute the values into the quadratic formula:
x = (-(-12) ± √((-12)^2 - 4 * 3 * 11)) / (2 * 3)

Simplifying further:
x = (12 ± √(144 - 132)) / 6
x = (12 ± √12) / 6
x = (12 ± 2√3) / 6

Simplifying the expression inside the parentheses:
x = (6 ± √3) / 3

So there are two solutions to the given quadratic equation:
1. x = (6 + √3) / 3
2. x = (6 - √3) / 3