Chapter A.3, Problem 126AYU

To determine

To find: The number that should be added to complete the square of each expression. Then factor each expression.

Answer to Problem 126AYU

$\frac{1}{36};{\left(x+\frac{1}{6}\right)}^2$

Explanation of Solution

Given:

$x^2+\frac{1}{3}x$

Calculation:

$x^2+\frac{1}{3}x+{\left(\frac{1}{2}.\frac{1}{3}\right)}^2=x^2+\frac{1}{3}x+\frac{1}{36}={\left(x-\frac{1}{6}\right)}^2$