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
FINAL ANSWER:
-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.