Solving Quadratic Equations by Completing the Square
Completing the square is another method for solving quadratic equations. We consider a general quadratic equation in which the coefficient of the leading term is not equal to one, in other words:
When we try to solve a quadratic equation by completing the square, we are looking for an equation of the form:
where h and d are constants. The completing the square method involves the following steps:
Step 1) Divide all terms by the coefficient of 
.
Step 2) Find 
Step 3) Find 
Step 4) Add 
to both sides of the equation.
Step 5) Complete the square on the left-hand-side of the equation.
Step 6) Keep the squared term on the left-hand-side and the constants on the right-hand-side.
Step 7) Take the square root of both sides and solve for the variable.
Example: Solve 
by completing the square.
Step 1) Divide all terms by 3:
Step 2) Divide the coefficient of x by 2:
Step 3) Square the number from Step 2):
Step 4) Add the number from Step 3) to both sides of the equation:
Step 5) Complete the square on the left-hand-side:
Step 6) Isolate the squared term on the left-hand-side of the equation:
Step 7) Take the square root of both sides and solve:
Check out this presentation by our Math Tutor Dr. Shohreh Rahmati about solving quadratic equations by completing the square.
