3.5 Solving Quadratic Equations by Completing the Square

3.5 Solving Quadratic Equations by Completing the Square

Solving by Square Root

If we can arrange a quadratic to be something squared on one side, and a number on the other:   $x^2-4=0$  

Also called the Square Root Property

The Special Quadratic:

• Remember

   $a^2\pm2ab+b^2=\left(a\pm b\right)\left(a\pm b\right)$  

• OR:  $\left(a\pm b\right)^2$  

• So now we can use this to solve in special cases

• Ex:  $x^2-8x+16=25$  

Let's do another

•  $4x^2-20x-25=32$  

Open Ended

Solve using the square root property:

 $x^2=9$  

Open Ended

Solve using the square root property:

 $2x^2-32=0$  

Open Ended

Solve by factoring then using the square root property:

 $x^2-18x+81=49$  

Open Ended

Solve by factoring then using the square root property:

 $25x^2+40x+16=28$  

Open Ended

Solve by factoring then using the square root property: 

$16x^2+24x+9=-81$