complete the square of the following expression 3-2x-x^2

Question

Please show the whole method and answer in my book is 4-(x+1)^2

Answer 1

(a ± b)² = a² ± 2ab + b²
3 - 2x - x² =
3 - (2x + x²) =
3 - (x² + 2 · 1 · x + 1² - 1²) =
3 - [(x² + 2x + 1) - 1] =  
3 - [(x + 1)² - 1] =
3 - (x + 1)² + 1 =     
4 - (x + 1)²

 

Answer 2

1) Rearrange the order to get ax^2 + bx + c.

-x^2 - 2x + 3

2) Identify a-value and factor it out of first two terms.

a = -1.

-(x^2 + 2x) + 3

3) Find value of (b/2)^2.

b = 2.  Therefor (b/2)^2 = 1.

4) Add and subtract (b/2)^2 into the equation. (This can be tricky)

-(x^2 + 2x +1 - 1) + 3

5) Use distributive property to remove 4th term from parentheses.

(-1*-1 = 1)

-(x^2 + 2x +1) + 1 + 3

6) Factor term in parentheses (It always factors down to (x+b/2)^2)

-(x+1)^2 + 4

Using the commutative property, this is equivalent to your book's answer.

Answer 3

3 - (2x  +  x^2)

= 3  +1  - (1  +  2x  +  x^2)

=    4     - (1 + x)^2