Solve Using the Square Root Property x^2=-4

Problem

x2=−4

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 and including both the positive and negative roots.

x=±√(,−4)

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

x=±√(,4)⋅√(,−1)

4. Evaluate the square root of 4 to find the final complex solutions.

x=±2*i

Final Answer

x=±2*i

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