Chapter 11.2, Problem 32E

To determine

To calculate:

The equation by completing square

  $5w-w^2=-11$

Answer to Problem 32E

The equation by completing square of $5w-w^2=-11$ is $w=\frac{5}{2}\pm \frac{\sqrt{69}}{2}$ .

Explanation of Solution

Given information:

  $5w-w^2=-11$

The given equation is:

  $5w-w^2=-11$

write equation in the standard form:

  $\begin{array}{l}-w^2+5w+11=0\\ w^2-5w-11=0\end{array}$

Comparing with the standard equation of $a{x}^2+bx+c=0$ :

  $\begin{array}{l}a=1\\ b=-5\\ c=-11\end{array}$

By quadratic formula:

  $n=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

So,

  $w=\frac{-5\pm \sqrt{{\left(-5\right)}^2-4\left(1\right)\left(-11\right)}}{2\left(1\right)}$

Simplify:

  $w=\frac{-5\pm \sqrt{69}}{2}$

Then, the required value of $w$ :

  $w=\frac{5}{2}\pm \frac{\sqrt{69}}{2}$