Question

the sides of a triangle have lengths of x, x+5, and 25. if the longest side is 25, which of the following values of x would make the right triangle?

Answer 1

When you see "... the following ...", that means there's supposed to be a list of choices.  I'll bet it was right there next to this question as you were copying, and you decided not to share it.

On paper or in the real world, 'x' must be 15 .

Mathematically, 'x' can also be -20 .

Answer 2

$x^2+5x-300=0 \\ \\ \Delta =b^2-4ac =5^2 -4*1* (- 300)= 25+1200=1225 \\ \\x_{1}=\frac{-b- \sqrt{\Delta } }{2a}=\frac{-5- \sqrt{1225}}{2 }=\frac{-5-35}{2}=-\frac{-40}{2}=-20 \\\\ \ side \ not \ can \ also \ be \ negative$

$x_{2}=\frac{-b+ \sqrt{\Delta } }{2a}=\frac{-5+ \sqrt{1225}}{2 }=\frac{-5+35}{2}=-\frac{30}{2}=15\\ \\Ansewr : \ x= 15$