Solve Using the Square Root Property x^2=-81

Problem

x2=−81

Solution

1. Identify the equation as a quadratic in the form x2=k where k is a constant.

2. Apply the square root property by taking the square root of both sides of the equation.

x=±√(,−81)

3. Simplify the square root of the negative number using the imaginary unit i where √(,−1)=i

x=±√(,81)⋅√(,−1)

4. Evaluate the square root of the perfect square 81

x=±9*i

Final Answer

x=±9*i

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