solve the following quadratic equation. round to the nearest hundredth if necessary: (x + 27)^2/-6 = -3

Question

enter the smaller of the 2 values first.

Answer 1

To solve the equation \(\frac{(x + 27)^2}{-6} = -3\), we first eliminate the fraction by multiplying both sides by \(-6\):

\[ (x + 27)^2 = -3 \times -6 \]

This simplifies to:

\[ (x + 27)^2 = 18 \]

Next, we take the square root of both sides:

\[ x + 27 = \pm \sqrt{18} \]

Calculating \(\sqrt{18}\) gives:

\[ \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \approx 3 \times 1.414 = 4.242 \]

Now, we have two equations:

1. \(x + 27 = 3\sqrt{2}\)
2. \(x + 27 = -3\sqrt{2}\)

Solving for \(x\):

1. For \(x + 27 = 3\sqrt{2}\):

\[ x = 3\sqrt{2} - 27 \approx 4.242 - 27 \approx -22.758 \]

2. For \(x + 27 = -3\sqrt{2}\):

\[ x = -3\sqrt{2} - 27 \approx -4.242 - 27 \approx -31.242 \]

Final values:

• The smaller value (rounded to the nearest hundredth) is approximately \(-31.24\).
• The larger value (rounded to the nearest hundredth) is approximately \(-22.76\).

Therefore, the smaller of the two values first:

\[ \boxed{-31.24} \quad \text{and} \quad \boxed{-22.76} \]