To rewrite: The expression x 2 + x + 1 by the method of completing square.

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

(a)

To determine

To rewrite: The expression x2+x+1 by the method of completing square.

Expert Solution

The expression x2+x+1 can be rewritten as, (x+12)2+34.

Explanation of Solution

Consider the expression x2+x+1.

Simplify the above expression as follows,

x2+x+1=x2+2×x×(12)+(12)2(12)2+1=(x+12)214+1((a+b)2=a2+2ab+b2)=(x+12)2+34

Thus, the expression x2+x+1 by completing square is (x+12)2+34.

(b)

To determine

To rewrite: The expression 2x2−12x+11 by the method of completing square.

Expert Solution

The expression 2x212x+11 can be rewritten as, 2(x3)27.

Explanation of Solution

Consider the expression 2x212x+11.

Simplify the above expression as follows,

2x212x+11=2(x26x)+11=2(x22×x×3+3232)+11=2((x3)29)+11((ab)2=a22ab+b2)=2(x3)218+11

=2(x3)27

Thus, the expression 2x212x+11 by completing square is 2(x3)27.

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