Chapter 9.5, Problem 52PFA

To determine

Find the solution.

Answer to Problem 52PFA

False

Explanation of Solution

Given Information: $x^2+bx=0$

Formula Used: $a^2+2ab+b^2={(a+b)}^2$ and $a^2-b^2=(a+b)(a-b)$

Calculation:

  $x^2+bx=0$

Now, adding the square of half the coefficient of x to complete he square.

  $x^2+bx+{\left(\frac{b}{2}\right)}^2=0$

Now use formula, $a^2+2ab+b^2={(a+b)}^2$

  ${\left(x+\frac{b}{2}\right)}^2=0$

So,

The statement given is false.

To complete the square, have to add ${\left(\frac{b}{2}\right)}^2$ to expression $x^2+bx=0$