Solve the following quadratic equation using square roots.
Round to the nearest hundredth if necessary: (x +27)^2/-6 - -3.
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To solve the quadratic equation (x +27)^2/-6 - -3, we can follow these steps:
1. Multiply -6 to both sides to eliminate the fraction:
(x + 27)^2 = (-6)(-3)
(x + 27)^2 = 18
2. Take the square root of both sides:
√[(x + 27)^2] = ± √18
3. Simplify the square root on the left side:
x + 27 = ± √18
4. Subtract 27 from both sides:
x = -27 ± √18
Therefore, the solutions to the quadratic equation are x = -27 ± √18.
Rounding to the nearest hundredth, we can use a calculator to find the approximate values:
x ≈ -27 + √18 ≈ -27 + 4.24 ≈ -22.76
x ≈ -27 - √18 ≈ -27 - 4.24 ≈ -31.24
Therefore, the solutions rounded to the nearest hundredth are x ≈ -22.76 and x ≈ -31.24.