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Solve x 2 + 8x -12 = 0 by completing the square

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Solve x2 + 8x -12 = 0

by completing the square

x2 + 8x =12

x2 + 8x + 16 =12 + 16

(x+ 4)2 =28

x+ 4 = +Ö 28

x=-4 +2Ö7 }

{ -4 +2Ö7 }

6.3: Relationship of Roots, Factoring, Graphing & Solving Equations

If A*B = 0 then

A= 0 or B = 0

Solve by factoring:

x2 – x - 6= 0

(x+2)(x-3) = 0

(x+2)=0 or (x-3) = 0

x= -2 or x=3

{-2, 3}

Equation:

Factors:

Solutions:

Roots:

Graph:

(x+2)(x-3)

{ -2,3}

-2 and 3

x-int at -2 and 3

MULT. and

make it = 0

Equation:

Factors:

Solutions:

Roots:

Graph:

(x-p)(x-q)

{p,q}

p and q

x-int at p and q

2x2 +7x = 15

Solve by

Factoring:

2x2 +7x – 15 = 0

(2x-3) (x+5) = 0

(2x-3)=0 or (x+5)= 0

2x=3 or x=-5

x=3/2 or x=-5

5x2 – 60=5x

Solve by

Factoring:

5x2 - 5x – 60 = 0

5(x2 - x – 12) = 0

5(x-4)(x+3)= 0

5=0 x-4=0 or x+3= 0

x=4 or x=-3

x2 + 5x = 0

Factors:

Solutions:

Roots:

Graph:

x(x+5)

{0,–5 }

0 and -5

x-int at 0 and -5

Write two equations that

has roots of ½ and –3/4

(x – ½)(x + 3/4 ) =0

x2 + 3x/4 – x/2 – 3/8 = 0

8 8 8

x2 + 1x/4 – 3/8 = 0

8x2 + 2x – 3 = 0

Find two consecutive odd

integers whose product is 195

x (x+2) = 195

x2 + 2x = 195

x2 + 2x – 195 = 0

(x-13)(x+15) =0

x-13 = 0 or x+15 =0

x=13 x=-15

13 & 15 or -15 &-13

2x2 +7x - 15

Factor by

graphing:

Roots: 3/2 and -5

Factors:(x – 3/2)(x+5)

(2x – 3) (x + 5)

Check:2x2 +7x - 15

4x2 - 100

Factor by

graphing:

4x2 - 100 =y

Roots: 5 and -5

Factors:(x – 5)(x+5)

Check: x2 – 25 NO!

4(x – 5) (x + 5)