Examine the expression (c -- 7)(c -- 2). To find the root, or the function of the variable c, write each of the binomials in the expression as an equation equal to zero: c -- 7 = 0 and c -- 2 = 0.
Move the constant term in the equation to the other side of the equation using the opposite property. In the first binomial, the constant 7 is subtracted; so use addition to move it. In the second binomial, the constant 2 is also subtracted and can be moved with addition.
Add 7 to both sides of the equation: c -- 7 + 7 = 0 + 7. Simplify the equation: c = 7. Add 2 to both sides of the equation: c -- 2 + 2 = 0 + 2. Simplify the equation: c = 2. Therefore, c has two solutions: c = 7, 2.
Examine the expression c^2 + 6c + 9. Factor the trinomial, which means simplifying the expression to binomials in parenthetical notation.
Find the square root of c^2 and 9: c^2 = c x c and 9 = 3 x 3. Since the terms are added, use addition in the parentheses: (c + 3)(c + 3).
Set the binomial to equal zero: c + 3 = 0. Because both binomials are the same, you only need to use one binomial. Subtract 3 from both sides of the equation and simplify: c + 3 -- 3 = 0 -- 3, which simplifies to c = -3.