What number should be added to complete the square: x^2+10x ?

Question

10, 5, 25 or 100?

Answer 1

25

Look at the general expression for the square of a binomial:

(x + a)^2 = x^2 + (2a)x + a^2

Notice that the last term is obtained by taking the number multiplying the x (ie. 2a), dividing it by 2, then squaring it.

So for the example above, the number multiplying the x is 10.  Divide it by 2 to get 5, then square it to get 25.

Answer 2

x^2 + 2ax + a^2 = (x + a)^2

so

x^2 + 10x + a^2 = (x + a)^2

would have 2a = 10

or a = 5

x^2 + 10x + 25 = (x + 5)^2

Ans = 25

Answer 3

25

halve the 10 and square it