Solve Using the Square Root Property x^2=-16

Problem

x2=−16

Solution

1. Identify the equation as being 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.

3. Include the plus-minus symbol to account for both the positive and negative roots.

x=±√(,−16)

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

x=±√(,16)⋅√(,−1)

5. Evaluate the square root of 16 to find the final complex solutions.

x=±4*i

Final Answer

x=±4*i

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