Question

the sum of a number and its square is 182. find the number

Answer 1

x(x+1)=182=13*14
x = 13

Answer 2

i would guess and check on this one. ten is too small because
\[10^2+10=110\] try something bigger.

Answer 3

Let x be this unknown number


So "the sum of a number and its square is 182" means that x+x^2 = 182, let's use this to solve for x


x+x^2 = 182


x^2+x = 182


x^2+x-182 = 0


Now use the quadratic formula to solve


x = (-b+-sqrt(b^2-4ac))/(2a)


x = (-1+-sqrt(1^2-4(1)(-182)))/(2(1))


x = (-1+-sqrt(729))/2


x = (-1+-27)/2


x = (-1+27)/2 or x=(-1-27)/2


x = 13 or x= -14


Assuming you want positive numbers only, the answer is x = 13


So the unknown number is 13


So the sum of 13 and its square 169 is 182