Completing the square

Question

m^2 - 1/2m = 7/2

Solve by completing the square.

(Type exact answers, using radicals as needed. Express complex numbers with i.)

Answer 1

m² - (1/2)m = 7/2

 

We want the left side of the equation to be a polynomial of a perfect square.  If we add 1/16 to both sides of equation, the left side will be a polynomial that is a perfect square.

 

 

m² - (1/2)m + (1/16) = (7/2) + (1/16)

 

(m - 1/4)(m - 1/4) = 57/16

 

(m - 1/4)² = 57/16

 

 

Now we square-root both sides of equation.

 

m - 1/4 = ±√(57/16)

 

m - 1/4 = ±√(57) / 4

 

m = (1/4) ± (√(57) / 4)

 

m = (1 ± √(57)) / 4

 

 

And there you have it. 

 

Now let me ask you this.  Does the solution here look like a certain formula that we use to solve a quadratic equation?