maths complete the square?

Question

1)5x^2 + 5x + 11

2)4x^2 + 7x -2

Answer 1

factor out the coefficient of X^2

seperate 1/2 of the X^1 coefficient squared

factor


like this....


5x^2 + 5x + 11 = 5 * (x^2 + x + 11/5)
1/2 of x coefficient = 1/2 * 1 = 1/2
1/2 squared = 1/4

5 * (x^2 + x + 11/5) = 5 * (x^2 + x + 1/4 + (11/5- 1/4))
= 5 * [(x^2 + x + 1/4) + 39/20]
5 * [(x+ 1/2)^2 + 39/20)]
= 5 (x+ 1/2)^2 + 39/4

and this....

4x^2 + 7x -2 = 4 * [x^2 + 7/4x -1/2]

but 1/2 x 7/4 = 7/8.
squared is 49/64

4 * [x^2 + 7/4x -1/2] = 4 * [x^2 + 7/4x +49/64 -(1/2- 49/64)]
= 4 * [x^2 + 7/4x + 49/64 - 81/64]
= 4 * [(x+ 7/8)^2 - 81/64]

Answer 2

1)5x^2 + 5x + 11
= 5(x^2 +x +11/5)
= 5(x^2+x +1/4)+11 -5/4
= 5(x+1/2)^2 + 9 3/4

2)4x^2 + 7x -2
You do this one because I'm not sure you are stating thes problems correctly. Are they supposed to be set = 0 and solved for x? If so you should say so.

Answer 3

1)5x^2 + 5x + 11

5(x² + 1x) + 11

(1/2 * 1)² = 1/4

5(x² + x + 1/4) + 11 - 5(1/4)

5(x + 1/2)² + 39/4

2)4x^2 + 7x -2

4(x² + 7/4 x) - 2

(1/2 * 7/4)² = 49/64

4(x² + 7/4 x + 49/64) - 2 - 4(49/64)

4(x + 7/8)² - 81/16

Answer 4

4(x^2 +(7/4)x)-2
4(x^2+(7/4)x+49/64-49/64)-2 (7/4 divided in half is 7/8)
4(x^2+(7/4)x+49/64)-49/16-32/16 (mult. 49/64 by the 4)
4(x+7/8)^2-81/16

Answer 5

http://answers.yahoo.com/search/search_result;_ylt=Aioy4M2f9xy8bccyntViaSoazKIX;_ylv=3?p=complete+the+square