Chapter 9, Problem 43SGR

To determine

To solve the given equation by completing the square.

Answer to Problem 43SGR

The values of a is null, since there are no real roots.

Explanation of Solution

Given information :

The function provided is $a^2-4a+9=0$ .

Formula used :

To solve an equation by completing the square, divide the coefficient of n of the equation by 2 and square it. That should provide the constant value. Then the equation would be of the form ${\left(x+\frac{b}{2}\right)}^2$ . Adjust the other constants and then square root the left-hand and right-hand sides. This would give the values of the equation.

Calculation :

  $a^2-4a+9=0$

Given equation

Here $b=-4$ , the coefficient of n.

  $\frac{b}{2}=-\frac{4}{2}$

For making the expression a perfect square.

  ${\left(\frac{b}{2}\right)}^2={\left(-\frac{4}{2}\right)}^2$

  $=4$

This is the value of the constant.

Make left hand side a perfect square using the value of b .

  $a^2-4a+4=-5$

Adjust the values accordingly

  $=>{\left(a-2\right)}^2=-5$

Since the right-hand side of the equation is a negative value, the square root cannot be obtained. This signifies that there are no real values of the equation.