Question

solve the following quadratic equation using square roots. round to the nearest hundredth if necessary (x+27+^/-6=-3

Answer 1

To solve the equation \( x + 27 \pm 6 = -3 \), we start by splitting it into two separate equations due to the \( \pm \) symbol.

1. First, we can set up the two cases:

- Case 1: \( x + 27 + 6 = -3 \)
- Case 2: \( x + 27 - 6 = -3 \)

### Case 1:
\[
x + 27 + 6 = -3
\]
Combine like terms:
\[
x + 33 = -3
\]
Now, isolate \( x \) by subtracting 33 from both sides:
\[
x = -3 - 33
\]
\[
x = -36
\]

### Case 2:
\[
x + 27 - 6 = -3
\]
Combine like terms:
\[
x + 21 = -3
\]
Now, isolate \( x \) by subtracting 21 from both sides:
\[
x = -3 - 21
\]
\[
x = -24
\]

### Summary of solutions:
The two solutions from the cases are:
\[
x = -36 \quad \text{and} \quad x = -24
\]

Thus, the solutions to the equation are \( x = -36 \) and \( x = -24 \).