Question

Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+27)2−6=−3
.(1 point)
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Answer 1

To solve the quadratic equation \((x + 27)^2 - 6 = -3\), we can first simplify the equation.

1. **Add 6 to both sides**:
\[
(x + 27)^2 - 6 + 6 = -3 + 6
\]
\[
(x + 27)^2 = 3
\]

2. **Take the square root of both sides**:
\[
x + 27 = \pm \sqrt{3}
\]

3. **Isolate \(x\)**:
\[
x = -27 \pm \sqrt{3}
\]

Now we have two possible solutions:
1. \(x = -27 + \sqrt{3}\)
2. \(x = -27 - \sqrt{3}\)

4. **Calculating the values**:
- For \(x = -27 + \sqrt{3}\):
\[
x \approx -27 + 1.732 \approx -25.268
\]

- For \(x = -27 - \sqrt{3}\):
\[
x \approx -27 - 1.732 \approx -28.732
\]

5. **Rounding to the nearest hundredth**:
- \(x \approx -25.27\)
- \(x \approx -28.73\)

Thus, the solutions to the equation are:
\[
x \approx -25.27 \quad \text{and} \quad x \approx -28.73
\]