Answer: second option.
Step-by-step explanation:
Given the following equation:
[tex](x+10)^2=256[/tex]
You need to find the value of "x" in order to find the side measure of the original square photo.
Knowing that:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
You can expand the equation:
[tex](x+10)^2=256\\\\x^2+2(x)(10)+10^2=256\\\\x^2+20x+100=256[/tex]
The next step is to subtract 256 from both sides of the equation:
[tex]x^2+20x+100-256=256-256\\\\x^2+20x-156=0[/tex]
Now you can factor the quadratic equation. Find two numbers whose sum is 20 and whose product is -156. These are 26 and 6:
[tex](x+26)(x-6)=0\\\\x_1=-26\\\\x_2=6[/tex]
Choose the positive value.
Therefore, the dimensions of the original square photo were:
[tex]6\ inches\ by\ 6\ inches[/tex]
