Answer: One of the numbers for which the given condition is true is 11 or -16.
Step-by-step explanation: Given that the square of a number increased by 5 times the number is equal to 176.
We are to find one number for which this can be true.
Let x be the number.
Then, according to the given information, we have
[tex]x^2+5x=176\\\\\Rightarrow x^2+5x-176=0\\\\\Rightarrow x^2+16x-11x-176=0\\\\\Rightarrow x(x+16)-11(x+16)=0\\\\\Rightarrow (x-11)(x+16)=0\\\\\Rightarrow x-11=0,~~~~~x+16=0\\\\\Rightarrow x=11,~-16.[/tex]
Thus, one of the numbers for which the given condition is true is 11 or -16.
