Solving Quadratics (completing square and quadratic formula)

 $a^2+10a+21=0$  

What is the first step to solving THIS equation by completing the square?

• Set the equation equal to zero

• Divide 10 by 2 and add the result to both sides

• Add a² and 10a together

• Subtract the 21

What do you do to the b value to correctly complete the square?

• square it
• divide it by 2 and square the result
• divide it by 2 and take the square root of the result
• divide it by 2 only

When do you use the plus or minus symbol?
±

• After taking the square root of both sides
• After adding the square to both sides
• After taking half of b
• After setting the equation equal to zero

 $x^2+6x=5$  

Write the quadratic equation above in completed square form...

•  $\left(x+3\right)^2=5$  

•  $\left(x+6\right)^2=9$  

•  $\left(x+3\right)^2=14$  

•  $\left(x+6\right)^2=14$  

 $x^2-10x-5=0$  

Solve the quadratic equation above by completing the square...

•  $x=-5\pm\sqrt{30}$  

•  $x=5\pm\sqrt{30}$ 

•  $x=30\pm\sqrt{5}$  

•  $x=-30\pm\sqrt{5}$  

 $x^2+6x-3=0$  

Solve the  quadratic equation above by completing the square...

• $-3\pm2\sqrt{3}$

• $3\pm2\sqrt{3}$

• $12\pm\sqrt{3}$

• $-12\pm\sqrt{3}$

 $x=\frac{-\left(b\right)\pm\sqrt{\left(b\right)^2-4\left(a\right)\left(c\right)}}{2\left(a\right)}$  

What is this formula?

• This is the speed of light formula.

• This is the quadratic formula.

• This is the zero product property.

• This is scary.

 $y=x^2+5x+7$  

In the equation above, match each leading coefficient with its correct letter 

• a=0, b=5, c=7

• a=1, b=5, c=7

• a=7, b=5, c=1

 $x^2+6x-13=3$  

What should you do first in solving this equation?

• Get factored form

• Write down: a=1, b=6, c=-13

• Make it equal 0 by subtracting 3 on each side

• Type it all in a calculator.

 $2x^2+7x-15=0$  

Solve Using the Quadratic Formula 

• -1.5 or 5

• No Solution

• -5 or 1.5

• 0.7 or 5