Solve Using the Square Root Property x^2=-64

Problem

x2=−64

Solution

1. Identify the equation as being in the form x2=k which allows for the use of the square root property.

2. Apply the square root property by taking the square root of both sides of the equation, remembering to include both the positive and negative roots.

x=±√(,−64)

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

x=±√(,64)⋅√(,−1)

4. Simplify the expression by evaluating the square root of 64

x=±8*i

Final Answer

x=±8*i

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