Shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. The area of the enlarged photo is 256 square inches. In the equation (x + 10)2 = 256, x represents the side measure of the original square photo.

Question

mathstudent55 · Answer

What is the question?
Do you need to solve for x, the length of the side of the original photo?

mathstudent55 · Answer

$(x + 10)^2 = 256$

$(x + 10)(x + 10) = 256$

$x^2 + 10x + 10x + 100 = 256$

$x^2 + 20x + 100 = 256$

$x^2 + 20x - 156 = 0$

$x + 26)(x - 6) = 0$

$x + 26 = 0$  or  $x - 6 = 0$

$x = -26$  or  $x = 6$

Since a square cannot have a side measuring a negative number, we discard the solution x = -26.

The answer is the original photo had a side of 6 inches.

Check:
Add 10 inches to a side of a square of 6 inches to get a side of 16 inches.
A square with a side of 16 inches has area A = s^2 = (16 in.)^2 = 256 in.^2
Our answer is correct.

sshayer · Answer

$$\left( x+10 \right)^2=256=\left( 16 \right)^2$$
$$x+10=\pm 16$$
$$either ~x+10=16,x=16-10=6$$
or x+10=-16
x=-16-10=-26 (rejected)
as side of square can not be negative.