Final answer:
In the perfect square trinomial x^2+12x+c, the formula for a perfect square trinomial is used to find 'c'. This involves determining the values of 'a' and 'b' that result in the coefficient of x, then using these values to calculate 'c'. The value of 'c' that makes x^2+12x+c a perfect square trinomial is 36.
Step-by-step explanation:
To find the value of c that makes x2+12x+c a perfect square trinomial, one method is to use the formula for a perfect square trinomial, which is (a+b)2=a2+2ab+b2.
In this case the coefficient of x, which is 12, is equal to 2ab. Since we are looking for a perfect square, a and b are going to be the same. Therefore, we have 2a*2*6=12, which gives a = 6.
Now, since b2 = c, if a = b = 6, we now have c= (6)2 = 36.
So the value of c that makes x2+12x+c a perfect square trinomial is 36.
Learn more about Perfect Square Trinomial