# I worked the problem out, but could you check my work over and see if it's correct? I used the quadratic formula.

2x^2+10x+11
a=2 b=10 c=11

x=-10(plus or minus) sqrt 10^2-4(2)(11)
over 2(2)

-10(plus or minus) sqrt 100 - 8(11)
over 4

-10(plus or minus) sqrt 100-88
over 4

-10(plus or minus) sqrt 12
over 4
-10(plus or minus) 2 sqrt 3
over 4

can this be simplified any more? or is the final answer even correct? pls help!!

Divide the 2a out, so

x= -2.5 +- .5* sqrt3

I'm a little confused. could you show me where exactly I went wrong? thanks! :)

When you used the formula
x = [-b +/- sqrt (b^2-4ac)]/2a, you forgot to divided by 2a, which is 4.

## To correct your work, let's go through the steps again.

You correctly identified the coefficients: a = 2, b = 10, and c = 11.

Using the quadratic formula, we have:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

x = (-10 ± √(10^2 - 4(2)(11))) / (2(2))

Simplifying further:

x = (-10 ± √(100 - 88)) / 4

x = (-10 ± √12) / 4

Now, let's simplify the square root of 12:

√12 = √(4 * 3) = 2√3

Substituting back into the equation:

x = (-10 ± 2√3) / 4

Next, let's simplify the expression further by factoring out a common factor of 2 in the numerator:

x = -2.5 ± (2/4)√3

Simplifying the fraction:

x = -2.5 ± (1/2)√3

Finally, we can express it in simplest form by multiplying the fraction by 2:

x = -2.5 ± (√3 / 2)

So, the correct final answer is:

x = -2.5 + (√3 / 2) OR x = -2.5 - (√3 / 2)

## To solve the quadratic equation 2x^2 + 10x + 11 = 0 using the quadratic formula, the correct steps are:

1. Identify the values of a, b, and c in the equation. In this case, a = 2, b = 10, and c = 11.

2. Plug these values into the quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / 2a.

3. Substitute the values: x = [-10 +/- sqrt(10^2 - 4(2)(11))] / (2 * 2).

4. Simplify inside the square root: x = [-10 +/- sqrt(100 - 88)] / 4.

5. Continue to simplify: x = [-10 +/- sqrt(12)] / 4.

At this point, let's further simplify the expression inside the square root. The number 12 can be factored as 4 * 3.

6. x = [-10 +/- sqrt(4 * 3)] / 4.

7. We can take the square root of 4, which is 2, out of the square root: x = [-10 +/- 2 * sqrt(3)] / 4.

Now, we can divide every term by 2 to simplify the expression further:

8. x = -5 +/- sqrt(3) / 2.

Finally, we can factor out 1/2 from the terms inside the square root:

9. x = -5 +/- (1/2) * sqrt(3).

So, the final answer is x = -5 +/- (1/2)sqrt(3).

Note: Don't forget to always divide the entire numerator by 2a (2 * 2 = 4 in this case) while using the quadratic formula.