Question

Evaluate the expression to the nearest hundredth. $$ \frac{-3 \pm 2 \sqrt{5}}{-1} $$

Short answer

The expression \(\frac{-3 \pm 2 \sqrt{5}}{-1}\) evaluates to -1.48 and 7.48 to the nearest hundredth.

Step-by-step solution

Evaluate the square root

The first step is to evaluate the square root \(\sqrt{5}\), which equals approximately 2.24.

Apply the plus-minus operation

After getting the square root result, you need to apply the plus-minus operation into the equation, which would give us two parts that need to be separately solved: \(\frac{-3 + 2 * 2.24}{-1}\) and \(\frac{-3 - 2 * 2.24}{-1}\).

Perform the multiplication

Next, perform the multiplication operation in both equations. This gives us \(\frac{-3 + 4.48}{-1}\) and \(\frac{-3 - 4.48}{-1}\).

Perform the addition and subtraction

Next step is to perform the addition in the first equation and subtraction in the second equation, resulting in the equations: \(\frac{1.48}{-1}\) and \(\frac{-7.48}{-1}\).

Perform the division

The final step is to complete the division operation, which yields -1.48 and 7.48 respectively.