What number must you add to complete the square x2 + 12x = -3

We must add number 36 to complete the square.

Step-by-step explanation:

Given  : x² + 12x = -3.

To find : What number must you add to complete the square.

Solution : We have given  that

x² + 12x = -3.

Step 1)  On multiplying and divide by 2 the term 12 x

x² + 2 *x = -3.

x² + 2 * 6x = -3.

Step 2 ) Now add and subtracting  square of 6 on left side.

x² + 2 * 6x + 6² - 6² = -3.

x² + 2 * 6x + 6²  - 36 = -3.

We can see first three terms are complete square

(x + 6 )² - 36 = -3 .

On adding both side by 36

(x + 6 )² = - 3 + 36

(x + 6 )² =  33.

Therefore, We must add number 36 to complete the square.

step-by-step explanation: