2.5.2 Solving Quadratic Equations by Square Root

Solving Quadratics by Square Root Property

Open Ended

What Do we know so far?  $$\sqrt[]{36}\ =$$  

Open Ended

Use expression "sqrt( )" for square root. Example: Write  $$\sqrt[]{9}$$  as sqrt(9) 

$$\sqrt[]{75}\ =$$  

To solve quadratic equations, we use inverse (opposite) operations

Multiple Choice

$$x^2=9$$  

What value of x makes the equation true?

• 3

• 9

• 81

• 4.5

Squares and Square Roots

Multiple Select

Solve

$$x^2=25$$  

• x=5

• x=-5

• x=525

• x=3

• x=-3

These equations have more than one answer!

Multiple Select

Solve

$$y^2=36$$  

• y=-6

• y=-9

• y=6

• y=9

• y=3

Example 1: Solving for x²

1. Distribute (if necessary)

2. Move your x² term to the left hand side

3. Move your constants to the right hand side (add 1 to both sides)

4. Divide the coefficient on both sides (if necessary)

5. Take the square root on both sides

6. End with 2 roots.

Example 2: Solving for x²

1. Distribute (if necessary)

2. Move your x² term to the left hand side

3. Move your constants to the right hand side (subtract 7 from both sides)

4. Divide the coefficient on both sides (divide by 3 on both sides)

5. Take the square root on both sides

6. End with 2 roots.

Multiple Choice

First step to solve this quadratic equation?

5m² + 1 = 6

• add 1 to both sides

• subtract 1 from both sides

• divide both sides by 5

• take the square root on both sides

Multiple Choice

Second step to solve this quadratic equation?

5m² + 1 = 6

• add 1 to both sides

• subtract 1 from both sides

• divide both sides by 5

• take the square root on both sides

Multiple Choice

Third step to solve this quadratic equation?

5m² + 1 = 6

• add 1 to both sides

• subtract 1 from both sides

• divide both sides by 5

• take the square root on both sides

Multiple Choice

What are the solution (s)? a.k.a. the roots

5m² + 1 = 6

• m = 1

• m = 1 or -1

• m = √7

• m = 7/5 m = -7/5

Multiple Choice

Solve by taking square roots.

x² +12 = 5

• x = ± 49

• No Real Solutions

• x = ± √7

• x = ± 5/12

Multiple Choice

$$x^2-5=31$$  

• $$\pm6$$  

• $$\pm36$$  

• $$\pm26$$  

• no real solution

Multiple Choice

Solve using square roots.

4m² - 100 = 0

• m=25, -25

• m=96

• m=5, -5

• m=-96

Multiple Choice

How many solution does a quadratic equation x² - 9 = 16 have ?

• none

• 1

• 2

• 3

Multiple Select

What are the roots / solutions of the quadratic equation (x+ 1)² = 50?

• $$x\ =\ -1\pm2\sqrt{25}$$

• $$x\ =\ 1\pm2\sqrt{25}$$

• $$x\ =1\pm\ 5\sqrt{2}$$

• $$x\ =\ -1\pm5\sqrt{2}$$