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 \( x = -24 \).