Question

Which of the following numbers must be added to complete the square in the equation below?

x^2 + 6x - 19 = 23

A.) 19

B.) -9

C.) 9

D.) 3

Answer 1

Completing the square Method :

The equation is x² + 6x - 19 = 23.

Separate variables and constants aside by adding 19 to each side.

x² + 6x - 19 + 19 = 23 + 19

x² + 6x = 42

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = 6. So, (half the x coefficient)² = (6/2)² = 3² = 9.

The option C is correct.