Solving Quadratic Equations – Square Root Method

• The square root method can be used to solve a quadratic equation that can be set up into the following form:

2(variable quantity) constant

• Examples: 2 8x 2( 5) 21x

2 16x 225(4 3) 20x

• An important property used to solve a quadratic equation by the square root method is given below.

Let y be an expression in variable x.

Principle of Square Roots

If 2y a

Then y a

y aor

This can also be written as y a

1. Get the variable quantity that is squared on the left side of the equation and the constant on the right side of the equation.

2. Take the square root of both sides. This step uses the Principle of Square Roots.

3. Solve for the variable.

Square Root Method to Solve Quadratic Equations

• Example 1:

Move the constant to the right side of the equation

Take the square root of both sides of the equation

Simplify

Solve the equation 2 16 0x 2 16x

2 16x

4x

• Example 2:

Move the constant to the right side of the equation

Take the square root of both sides of the equation

Solve for the variable

Solve the equation2( 3) 5 0x

2( 3) 5x

3 5x

3 5x

• Example 3:

Move the constant to the right side of the equation

Take the square root of both sides of the equation

Solve for the variable

Solve the equation2( 2) 8 0x

2( 2) 8x

2 8x

2 2 2x i

2 2 2x i

• Example 4:

Since the constant is already on the right side, and 25 is a perfect square, take the square root of both sides

Solve the equation225(4 3) 20x

5(4 3) 20x

5(4 3) 2 5x

Solve for the variable 20 15 2 5x

20 15 2 5x

15 2 5

20x

5(4 3) 2 5x