Solving Quadratic Equations by Completing the Square

The equation must be in standard form:
ax² + bx + c = 0

For example:
Solve the equation by completing the square:
2x² +12x + 3 = 0
Therefore a = 2, b = 12, and c = 3

Step 1

If a = 1, then go on to Step 2. Otherwise, divide both sides of the equal sign by a .

Since a is not equal to 1. . .
Divide every term by 2... ... to get

Step 2

Get all variable terms on one side of the equation and all constants on the other side.

Step 3

Complete the square for the resulting binomial by adding to both sides of the equation.

b. Divide the 6 by 2 in the parentheses
c. Square the resulting 3 and add it to both sides
d. Convert 9 to a fraction to add constants on right side of equation
e. Add the fractions on the right side of the equation 

Step 4

Factor the resulting perfect square trinomial and write it as the square of a binomial.

Step 5

Use the square root property to solve for x.

a. Take the square root of both sides of the equation ... ...to get

b. Subtract 3 from both sides to isolate the variable

c. This leaves the final answers of and

Practice Exercises:

Answers: