TUTORIALS:

Solving Quadratic Equations by Completing the
Square
Now, we will complete the square to solve a quadratic equation.
For example, letâ€™s solve: 
x^{2} + 2x = 4 
We begin on the leftside of the equation by completing the square.
To find the number needed to complete
the square for x^{2} + 2x, calculate
where b
= 2. 

Thus, to complete the square for x^{2} + 2x, we add 1.
However, we are working with an
equation, so we must add 1 to both
sides of the equation.

x^{2} + 2x + 1 
= 4 + 1 
The left side can be written as the
square of a binomial. 
(x + 1)^{2} 
= 5 
To solve this equation, use the
Square Root Property:



For each equation, subtract 1
from both sides. 


So, the two solutions of x^{2} + 2x = 4 are
We can write the solutions using shorthand notation:
Here is a procedure we can use to solve any quadratic equation.
Note:
The symbol Â± is read â€œplus or minus.â€
Procedure â€” To Solve a Quadratic Equation by Completing the Square
Step 1 Isolate the x2term and the xterm on one side of the
equation.
Step 2 If the coefficient of x^{2} is not 1, divide both sides of the
equation by the coefficient of x^{2}.
Step 3 Find the number that completes the square:
â€¢ Multiply the coefficient of x by
.
â€¢ Square the result.
Step 4 Add the result of Step 3 to both sides of the equation.
Step 5 Write the trinomial as the square of a binomial.
Step 6 Finish solving using the Square Root Property.
Step 7 Check each solution.
