Answer:
The integer is 1
Step-by-step explanation:
Required
Translate and solve
Let the positive integer be x.
So, we have;
The square of the integer is: x^2
Plus 5 times its consecutive integer is: x^2 + 5(x + 1)
Equals 11 is: x^2 + 5(x + 1) = 11
So, we have:
[tex]x^2 + 5(x + 1) = 11[/tex]
Open bracket
[tex]x^2 + 5x + 5= 11[/tex]
Subtract 11 from both sides
[tex]x^2 + 5x -6= 0[/tex]
Expand
[tex]x^2 + 6x - x-6= 0[/tex]
Factorize:
[tex]x(x + 6) - 1(x+6)= 0[/tex]
Factor out x + 6
[tex](x - 1) (x+6)= 0[/tex]
Split
[tex]x - 1 = 0\ or\ x + 6 = 0[/tex]
Solve for x in both cases
[tex]x = 1\ or\ x = -6[/tex]
Since the number is positive, then [tex]x = 1[/tex]
