Find the Value of c that expression is a perfect-square Trinomial
m^2 - 6m + c = 30 + c
a. c = 9
b. c = 36
c. c = 3
d. c = 6
To find the value of c that makes the expression a perfect square trinomial, we need to complete the square.
Start by moving the constant term to the other side of the equation:
m^2 - 6m + c - c = 30
Now factor out the m terms on the left side:
m^2 - 6m + c - c = 30
m^2 - 6m + (c - c) = 30
Now we want to think of c as b/2 in the perfect square trinomial formula: a^2 - 2ab + b^2 = (a-b)^2. We can see that b = -6 in our case, so it would be best if c - c = (-6)^2:
m^2 - 6m + 9 = 30
Now this forms a perfect square trinomial that can be factored into (m - 3)^2. So the value of c that makes the expression a perfect square trinomial is c = 9.
Therefore, the answer is:
a. c = 9