Question

Complete the square: x2+7x+?=(x+?)2

Answer 1

x² + 7x + 12.25 = (x+3.5)²

Explanation:

(a+b)² = a²+ 2ab + b²

then:

7x = 2ab

7/2 = 3.5

then:

(x+3.5)² = x² + 2*3.5*a + 3.5²

x² + 7x + 12.25 = (x+3.5)²

Answer 2

x² + 7x + 49/4 = (x + 7/2)²

Explanation:

x² + bx + c is a perfect square when c = (b/2)².

b = 7, c = (7/2)² = 49/4.

x² + 7x + 49/4 = (x + 7/2)²