SOLUTION: Each side of a square is increased 6 inches. When this happens, the area is multiplied by 25. How many inches in the side of the original square?

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Question 964085: Each side of a square is increased 6 inches. When this happens, the area is multiplied by 25. How many inches in the side of the original square?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
s=original side
%28s%2B6%29%5E2=25s%5E2
s%5E2%2B12s%2B36=25s%5E2 Subtract 25s^2 from each side.
-24s%5E2%2B12S%2B36=0 Divide each side by -12.
2s%5E2-s-3=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation as%5E2%2Bbs%2Bc=0 (in our case 2s%5E2%2B-1s%2B-3+=+0) has the following solutons:

s%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A2%2A-3=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+25+%29%29%2F2%5Ca.

s%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+25+%29%29%2F2%5C2+=+1.5
s%5B2%5D+=+%28-%28-1%29-sqrt%28+25+%29%29%2F2%5C2+=+-1

Quadratic expression 2s%5E2%2B-1s%2B-3 can be factored:
2s%5E2%2B-1s%2B-3+=+2%28s-1.5%29%2A%28s--1%29
Again, the answer is: 1.5, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-1%2Ax%2B-3+%29

So s=1.5 inches.
ANSWER: The sides of the original square were 1.5 inches.
CHECK:
Original area=%281.5in%29%5E2=2.25in%5E2
%281.5in%2B6in%29%5E2=25%282.25in%5E2%29
%287.5in%29%5E2=56.25in%5E2
56.25in%5E2=56.25in%5E2