SOLUTION: If the side length of a square can be represented by 2x + 10 and its area is 256 square units, find the value of x.

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Question 463216: If the side length of a square can be represented by 2x + 10 and its area is 256 square units, find the value of x.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

If the side length of a square can be represented by 2x+%2B+10 and its area is 256units%5E2, find the value of x.
the area is %282x+%2B+10%29%282x+%2B+10%29=256units%5E2
4x%5E2%2B20x%2B20x+%2B+100=256units%5E2
4x%5E2%2B40x+%2B+100-256units%5E2=0

4x%5E2%2B40x-156units%5E2=0...use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-40+%2B-+sqrt%28+40%5E2-4%2A4%2A%28-156%29+%29%29%2F%282%2A4%29+
x+=+%28-40+%2B-+sqrt%28+1600%2B2496%29%29%2F8+
x+=+%28-40+%2B-+sqrt%28+4096%29%29%2F8+
x+=+%28-40+%2B-+64%29%2F8+
use only positive solution because the length cannot be negative

x+=+%28-40+%2B+64%29%2F8+
x+=+24%2F8+
x+=+3+


so, the length is: 2x+%2B+10 ....->...2%2A3+%2B+10=6%2B10=16units
the area is16units%2A16units=256units%5E2