Question

Amira is solving the equation x^2-8x=7. Which value must be added to both sides of the equation to make the left side a perfect-squared trinomial?

Answer 1

16

Explanation:

The constant in a perfect square trinomial is the square of half the coefficient of the linear term.

(x +a)² = x² +2ax +a²

For 2a=-8, a=-4 and a² = 16. The constant 16 must be added:

x² -8x +16 = 7+16 . . the left side is a perfect square trinomial

(x -4)² = 23 . . . . . . . the left side is a perfect square