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

Question

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Enter the smaller of the 2 values first.

Answer 1

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

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

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

3. Now, solve for \( x \): \[ x = -27 \pm \sqrt{3} \]

This gives us two solutions: \[ x_1 = -27 + \sqrt{3} \] \[ x_2 = -27 - \sqrt{3} \]

4. Calculate the numerical values of \( x_1 \) and \( x_2 \): \[ \sqrt{3} \approx 1.732 \] So, \[ x_1 \approx -27 + 1.732 \approx -25.268 \] \[ x_2 \approx -27 - 1.732 \approx -28.732 \]

5. Rounding to the nearest hundredth: \[ x_1 \approx -25.27 \] \[ x_2 \approx -28.73 \]

6. Therefore, the smaller value first: \[ \boxed{-28.73} \quad \text{(smaller value)} \] \[ \boxed{-25.27} \quad \text{(larger value)} \]