*Completing the Square*

Solving Using Square Roots

100

Use square roots to solve the quadratic equation

x² + 12x + 36 = 25

x = -11 and x = -1

200

Use square roots to solve the quadratic equation

x² - 10x + 25 = 144

x = 17 and x = -7

300

Use square roots to solve the quadratic equation

x^2+6x+9=49/4

x = 1/2  , x = -13/2

400

Use square roots to solve the quadratic equation

x^2-22x+121=225

x = -4 , x = 26

500

Use square roots to solve the quadratic equation

50=2x^2+16x+32

x = -9 , x = 1

Completing the Square

100

Rewrite

x^2+4x+3=0

in the form 

(x-p)^2=q

(x+2)^2=1

200

Rewrite

x^2-6x+13=0

in the form 

(x-p)^2=q

(x-3)^2=-4

300

Rewrite

0=x^2-18x+64

in the form 

(x-p)^2=q

(x-9)^2=17

400

Rewrite

0=4x^2+4x-14

in the form 

(x-p)^2=q

(x+1/2)^2=15/4

500

Rewrite

x^2+0.6x-19.1=0

in the form 

(x-p)^2=q

(x+0.3)^2=19.19

Solving by completing the square

100

Solve by completing the square

x^2+10x-1=0

x=-5+sqrt26

x=-5-sqrt26

200

Solve by completing the square

x^2+2x-7=0

x=-1+2sqrt2

x=-1-2sqrt2

300

Solve by completing the square

-x^2+6x+10=0

x=3+sqrt19

x=3-sqrt19

400

Solve by completing the square

x^2+5x=3x+11

x=-1+2sqrt3

x=-1-2sqrt3

500

Solve by completing the square

5x^2-25=10x

x=1+sqrt6

x=1-sqrt6

Write in Vertex Form

100

Write the equation in vertex form

y=x^2-6x+4

y=(x-3)^2-5

200

Write the equation in vertex form

y=x^2+14x+50

y=(x+7)^2+1

300

Write the equation in vertex form

y=3x^2+8x+2

y=3(x+4/3)^2-10/3

400

Write the equation in vertex form

y=-2x^2+6x-2

y=-2(x-3/2)^2+5/2

500

Write the equation in vertex form

y=x^2-14x+71

y=(x-7)^2+22