Answer
b = 6 and b = -6
Work Step by Step
In a perfect square trinomial, in th form $ax^{2} + bx + c$, the constant (c) is equal to the square of half the coefficient of the second term, b.
$c = (\frac{b}{2})^{2}$
Substitute c with 9 and solve for b.
$9= (\frac{b}{2})^{2}$
To undo the square, we need to take the square root of 9, which will equal to either positive 3 or negative 3. In this case, we will split this off into two equations to solve for the two possible values for the second term coefficient.
$3 = \frac{b}{2} $ and $ -3 = \frac{b}{2}$
Solve for b by multiplying both sides of the equation by 2.
b = 6 and b = -6
