Question

What number must you add to complete the square? x^2+26x=33

Answer 1

Answer:

Must add: 202

Step-by-step explanation:

$The \ formula \ for \ perfect \ square => (a + b)^2 = a^2 + 2ab + b^2$

a = x

2ab = 26x

2ab = 26a  [ substitute a instead of x]

$b = \frac{26a}{2a}$

b= 13

So,

  $(x + 13)^2 = x^2 + 26x + 169$

But given equation is :

       $x^2 + 26x = 33\ => \ x^2 + 26x -33 = 0$

We have find the difference between 169 and -33 to get the number that should be added to get the perfect square.

That is , 169 - (-33) = 202

Therefore ,

   $x^2 + 26x -33 + 202 \ makes \ given \ equation \ a \ perfect \ square$