Complete the square by writing S2 12S 13 in the form S h2

Complete the square by writing S² + 12S - 13 in the form (S - h)² +K. Note: the numbers h and K can be positive or negative.

S² + 12S - 13 = (_______) + _______

Solution

Solution: To write S² + 12S - 13 in the form (S - h)² +K, we may write as:

S² + 2(6)S - 13

Now adding and subtracting 6^2, to get

S² + 2(6)S +6^2 - 13 - 6^2

= (S+6)^2-13+36

= (S+6)^2+23

Therefore S² + 12S - 13 = (S+6)^2 + 23.                             Ans.