Thanks for your help in advance. The area of a square with side 2x-1 is 49. Find x.

Expert Answers
lemjay eNotes educator| Certified Educator

To solve for the value of x, apply the formula of area of square.

`A= s^2`

where s represents the length of the side of the square.

So, plug-in A=49 and s=2x-1 to the formula.


Then, expand right side of the equation.


Set one side of the equation equal to to zero. To do so, subtract both sides by 49.



To simplify, divide both sides by the GCF of 4x^2-4x-48.




Then, factor.


Then, set each factor equal to zero and solve for x.

For the first factor:




And for the second factor:




To determine which of these two values of x should be considered as the solution, plug-in the values to 2x-1. But, take into consideration that 2x-1 represents the length of the side of the square. So, the resulting value should be positive (greater than 0).

For the first value x=4:

`2x - 1gt0`

`2(4) - 1gt0`

`7gt 0`               (True)

For the second value x=-3:

`2x - 1gt0`


`-7gt0`            (False)

Hence, the value of x in a square that has a side 2x-1 and an area of 49 is 4  `(x=4)` . 

embizze eNotes educator| Certified Educator

The area of a square can be found by `A=s^2` where A is the area and s the side length.

Here A=49 and s=2x-1 so:






So x=4 or -3. Since the value of 2x-1 has to be positive (all lengths are nonnegative) we take x=4.


The solution is x=4


Check: 2(4)-1=7 and 7*7=49

It might be easier to do this problem if you realize that if the area is 49, the sides must be 7. Then 2x-1=7 ==> x=4