Question

If using the method of completing the square to solve the quadratic equation x^2-11x-14=0, which number would have to be added to "complete the square"?

Answer 1

30.25

Explanation:

Solving :

• x² - 11x - 14 = 0
• To complete the square, we need to add and subtract a specific number (n²)
• The middle term in a perfect square trinomial is : 2ab
• Hence, 2(1)(n) = -11
• ⇒ n = 11/2 = -5.5
• Therefore, the number which has to be added (and subtracted) is :
• ⇒ (-5.5)²
• ⇒ 30.25

Answer 2

(11/2)² also known as 30.25

Using the (b/2)² formula, we can base this problem off of that method to solve the equation.

Explanation:

(x - 11/2)² - 177/4 = 0 ⇒ Completing the square