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

Question

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

3. Calculating the values:

   • For \(x = -27 + \sqrt{3}\): \[ x \approx -27 + 1.732 \approx -25.268 \]

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

4. Rounding to the nearest hundredth:

   • \(x \approx -25.27\)
   • \(x \approx -28.73\)

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