Solving Equations with Squares

Solving Quadratic Equations by Square Root

Solving for the x² term

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First things First

Lets Review FOIL Method

Multiple Choice

• 5x²+16x+8

• 6x²+12x+8

• 6x²+16x+6

• 6x²+16x+8

Multiple Choice

• x²+6x-16

• x²+10x-16

• x²+6x+16

• x²-6x-16

Lets Move on

Lets solve for x² using square roots.

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.

Your Turn

Lets see if you've been paying attention.

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 using square roots.

4m² - 100 = 0

• m=25, -25

• m=96

• m=5, -5

• m=-96

Multiple Choice

$$x^2-5=31$$  

• $$\pm6$$  

• $$\pm36$$  

• $$\pm26$$  

• no real solution

Multiple Choice

Solve by taking square roots.

x² +12 = 5

• x = ± 49

• No Real Solutions

• x = ± √7

• x = ± 5/12

Multiple Choice

Solve using square roots.

k² - 6 = 43

• k = √37

• k = 37 or - 37

• k = 7, k = -7

• no real solution

Multiple Choice

Solve:

x² - 49 = 0

• x = -7, x = 7

• x = -7

• x = 7

• x = -7, x = 1

Multiple Choice

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

• none

• 1

• 2

• 3

Poll

Solving Quadratic Equations, How you feeling right now?