SOLUTION: what is 7 plus or minus the square root of 24 over 2?

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Question 84041: what is 7 plus or minus the square root of 24 over 2?

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Presuming that you don't mean that only the square root of 24 is divided by 2, your problem
is to find:
.
%287%2B-sqrt%2824%29%29%2F2
.
This has two answers ... one answer involves the plus sign and the other answer involves
the minus sign. In other words, the answers to your question are:
.
%287%2Bsqrt%2824%29%29%2F2 and %287-sqrt%2824%29%29%2F2
.
You can find sqrt%2824%29 using a calculator. You should find that sqrt%2824%29=+4.898979486
.
Substituting that number for sqrt%2824%29 in the two answers results in the two answers
becoming:
.
%287%2B4.898979486%29%2F2 and %287-4.898979486%29%2F2
.
In the first answer the two terms in the numerator add to give 11.898979486 so this answer
becomes:
.
11.898979486%2F2 and dividing the 2 into the numerator of 11.898979486 results
in that answer becoming:
.
11.898979486%2F2+=+5.949489743
.
In the second answer the two terms of the numerator are subtracted. This subtraction
(7 - 4.898979486) results in 2.101020514. Substituting this value for the numerator
of the second answer, results in the second answer becoming:
.
2.101020514%2F2+=+1.050510257
.
In summary, your original problem has two answers:
.
5.949489743 and 1.050510257
.
Hope this work helps you to understand how to evaluate expressions of the form that you
have in this problem.