Question

What number must you add to complete the square ? x^2-18x=29

Answer 1

`x^2 - 18x + ( (18)/(2))^2 =29 + ( (18)/(2))^2`


`x^2 - 18x + (9)^2 =29 + (9)^2`


`(x - 9)^2 = 119`

The number to add is 9² which is 81.

Answer: 81

Answer 2

Answer: The required number to be added is 81.

Step-by-step explanation: We are given to find the number that must be added to both sides of the equation below to complete the square.

`x^2-18x=29~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

Completing the square means adding a suitable number to an expression such that is becomes a perfect square trinomial.

We have from equation (i) that

`x^2-18x=29\\\\\Rightarrow x^2-* x*9=29\\\\\Rightarrow x^2-2* x* 9+9^2=29+9^2\\\\\Rightarrow (x+9)^2=29+81\\\\\Rightarrow (x+9)^2=110.`

Thus, the required number to be added is 81.