Chapter 9.6, Problem 10P

Use the quadratic formula to solve each equation. Round answers to the nearest hundredth.

$h^2-2h-2=0$

To determine

To solve : The quadratic equation using quadratic formula and round the answer to the nearest hundredth.

Answer to Problem 10P

The solution for the equation is $h=2.73$ and $h=-0.73$

Explanation of Solution

Given information :

The given equation is $h^2-2h-2=0$ .

Calculation :

For the quadratic equation $a{x}^2+bx+c=0$ the quadratic formula is

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Now, for the given equation

  $h^2-2h-2=0$

  $a=1$ , $b=-2$ and $c=-2$ .

Therefore,

  $\begin{array}{l}h=\frac{-\left(-2\right)\pm \sqrt{{\left(-2\right)}^2-4\left(1\right)\left(-2\right)}}{2\left(1\right)}\\ h=\frac{2\pm \sqrt{4+8}}{2}\\ h=\frac{2\pm \sqrt{12}}{2}\\ h=\frac{2\pm 2\sqrt{3}}{2}\\ h=1\pm \sqrt{3}\\ h=1+\sqrt{3}\mathrm{and}h=1-\sqrt{3}\\ h=2.73\text{ and }h=-0.73\end{array}$

Hence,

The solution for the equation is $h=2.73$ and $h=-0.73$