SOLUTION: If you subtract a number from the half of its square, you get 11. What are the two possible values. Indicate the exact values and then calculate the approximate values

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: If you subtract a number from the half of its square, you get 11. What are the two possible values. Indicate the exact values and then calculate the approximate values       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1062169: If you subtract a number from the half of its square, you get 11. What are the two possible values. Indicate the exact values and then calculate the approximate values
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the unknown number
+n%5E2%2F2+-+n+=+11+
Multiply both sides by +2+
+n%5E2+-+2n+=+22+
Complete the square
+n%5E2+-+2n+%2B+%282%2F2%29%5E2+=+22+%2B+%282%2F2%29%5E2+
+n%5E2+-+2n+%2B+1+=+23+
+%28+n+-+1+%29%5E2+=+%28sqrt%2823+%29%29%5E2+
Take the square root of both sides
+n+-+1+=+sqrt%2823%29+
+n+=+1+%2B+sqrt%2823%29+
and, taking the negative square root of +23+,
+n+-+1+=+-sqrt%2823%29+
+n+=+1+-+sqrt%2823%29+
-----------------------
Approximate values:
+n+=+1+%2B+4.7958+
+n+=+5.7958+
and
+n+=+1+-+4.7958+
+n+=+-3.7958+
------------------------
Here's the plot:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-30%2C+5%2C+x%5E2+-+2x+-+22+%29+