Question

Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x + 16 ) 2/9 = 7
.(1 point)
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Note: Write your answer in set notation.

Answer 1

Let y = x + 16. Then (y^{1/9})^2 = 7, so y^{1/9} = ±√7 and y = (±√7)^9 = ±7^{9/2} = ±2401√7.

Thus x = ±7^{9/2} − 16. Numerically,
x ≈ 6352.4488978660823 − 16 = 6336.45 and x ≈ −6352.4488978660823 − 16 = −6368.45.

In set notation: {2401√7 − 16, −2401√7 − 16} ≈ {6336.45, −6368.45}.