Aquadratic equation is shown below:

x2 − 14x + 41 = 0

which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers? (5 points)

a: add 8 to both sides of the equation
b: add 9 to both sides of the equation
c: subtract 8 from both sides of the equation
d: subtract 9 from both sides of the equation

Since the desired equation is a perfect square binomial, it is necessary to obtain a constant term (in the case of the given equation, 41) that is also a perfect square. To determine the perfect square needed, take the coefficient of the second term (14x) and divide it by two, then square it. It should yield "49". To obtain 49 as the constant term, we have to add 8 to both sides of the equation. Among the choices, the correct answer is A.

Base times height divided by two