Respuesta :
[tex]x^2 - 18x + ( \frac{18}{2})^2 =29 + ( \frac{18}{2})^2[/tex]
[tex]x^2 - 18x + (9)^2 =29 + (9)^2[/tex]
[tex](x - 9)^2 = 119[/tex]
The number to add is 9² which is 81.
Answer: 81
[tex]x^2 - 18x + (9)^2 =29 + (9)^2[/tex]
[tex](x - 9)^2 = 119[/tex]
The number to add is 9² which is 81.
Answer: 81
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.
[tex]x^2-18x=29~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
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
[tex]x^2-18x=29\\\\\Rightarrow x^2-\times x\times9=29\\\\\Rightarrow x^2-2\times x\times 9+9^2=29+9^2\\\\\Rightarrow (x+9)^2=29+81\\\\\Rightarrow (x+9)^2=110.[/tex]
Thus, the required number to be added is 81.
