Math Problem Statement
Solution
To solve the equation using the square root property, we first need to take the square root of both sides.
Starting with the given equation: Step 1: Apply the square root property. Take the square root of both sides.
Step 2: Notice that involves a negative number under the square root, so we can express this as a complex number. Recall that , where is the imaginary unit.
Step 3: Isolate by subtracting 5 from both sides.
Thus, the solution to the equation is:
Would you like a more detailed breakdown or further explanation of any step? Here are some follow-up questions that might help:
- What is the square root property and how is it used to solve equations like this one?
- Can you explain why we end up with imaginary numbers in this equation?
- What is the significance of the complex number ?
- How do you simplify the square root of negative numbers in general?
- How would you check the solutions to this equation?
Tip: Whenever you encounter a negative number under a square root, you know the solution will involve imaginary numbers, so be prepared to deal with .
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Math Problem Analysis
Mathematical Concepts
Square Root Property
Complex Numbers
Imaginary Unit
Formulas
√(a*b) = √a * √b
√-1 = i
Theorems
Square Root Property
Imaginary Numbers
Suitable Grade Level
Grades 9-12