x²-14x-5=0

Question

Solve the quadratic equation by completing the square

Answer 1

When completing the square, we want a polynomial on one side of the equation to be a perfect square.  Since the left side of equation already has an x² and x term, we can tell that this side of equation can be turned into a perfect square.

 

Add 54 on both sides of equation.

 

x² - 14x - 5 + 54 = 0 + 54

 

x² - 14x + 49 = 54

 

(x - 7)(x - 7) = 54

 

(x - 7)² = 54

 

 

Square-root both sides of equation to undo the exponent on the left side.

 

x - 7 = ±√(54)

 

 

Add 7 on both sides of equation.

 

x = 7 ± √(54)

 

x = 7 ± √9 √6

 

x = 7 ± 3√6

 

 

x = 7 - 3√6             and              x = 7 + 3√6

 

 

Now ask yourself this question:  Does the form of the solutions remind you of the quadratic formula?