Chapter 9.1, Problem 2AYU

To complete the square of $x^2+6x$, add ______ .

To determine

To fill: To complete the square of $x^2+6x$, add _____.

Answer to Problem 2AYU

To complete the square of $x^2+6x$, add $3^2=9$.

Explanation of Solution

Formula used:

${\left(a+b\right)}^2=a^2+b^2+2ab$

Calculation:

a. Split $6x$ in the form of $2.a.b$ so that means $6x$ can written as $2\times 3$.

b. Here $a=x,b=3$.

c. Now to complete the given square we have to add $3^2$ to given equation, that means we have to add 9 to the given equation.

d. Now square can be reduced to ${\left(x+3\right)}^2$.

$x^2+2\text{ \&*\#x00A0;}3\text{ \&*\#x00A0;}x+3^2={\left(x+3\right)}^2$