Question

Find the term that must be added to the equation x2−8x=3 to make it into a perfect square. A. -3 B. 16 C. 64 D. 32

Answer 1

B. 16

Explanation:

The linear term of a perfect square quadratic trinomial is twice the product of the roots of the leading term and the constant. That means the constant is the square of half the coefficient of the linear term.

Completing the square

The coefficient of the linear term is -8. The square of half that is ...

(-8/2)² = 16

The constant that must be added is 16:

x² -8x +16 = 3 +16

(x -4)² = 19