Find the Value of c such that the expression is a perfect-square Trinomial m2−6m+c=30+c
To make the expression a perfect-square trinomial, we need to find the value of c such that it can be factored into the form (m - n)^2.
Given expression: m^2 - 6m + c = 30 + c
To find the value of c, we need to complete the square. First, take half of the coefficient of m and square it.
Half of the coefficient of m = -6/2 = -3
(-3)^2 = 9
Add and subtract 9 to the expression:
m^2 - 6m + 9 - 9 + c = 30 + c
(m - 3)^2 - 9 + c = 30 + c
Now, our perfect-square trinomial is:
(m - 3)^2 - 9
We need the constant term that goes with the square to equal the constant term on the other side of the equation.
-9 = 30
c = -9
Therefore, the value of c that makes the expression a perfect-square trinomial is c = -9.