How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions?

Subtract 38 from both sides to isolate x²
The symbol above the x² and -36 is the square root symbol
'±' means 'plus or minus'
We have a '±' to account for both the positive and negative square roots of -36
Factoring out the -1 from -36 will allow us to deal with just the positive part of the square root
The Product Property of Square Roots splits the square root into the product of two square roots
'i' is the imaginary unit and is equal to the square root of -1

1. There are multiple methods to solve a quadratic equation
1. There are multiple methods to solve a quadratic equation
2. Since there is no 'x' term, we can use the square root method
1. The first step in solving for 'x' is to get x² by itself
2. The Subtraction Property of Equality allows us to subtract 38 from both sides
3. On the right we have 2-38 = -36
4. On the left we have x²+38-38 = x²
1. Taking the square root of both sides will get rid of the square on the x²
1. Squaring the negative version of a number gives you the same result as squaring the positive version
2. For example, squaring 6 and -6 will both give you 36
3. So the square root of 36 could be either positive or negative
4. Check out the Square Root Property to learn more
1. We still have a perfect square term under the square root symbol, so we can simplify this further!
1. We can rewrite √(-1•36) as two radicals multiplied together:
2. The square root of -1 and the square root of 36, or √(-1)•√(36)
1. 'i' is the imaginary unit and is equal to the square root of -1
2. 'i' is NOT a variable!
3. The symbol above the -1 and 36 is the square root symbol
4. '±' means 'plus or minus'
5. The square root of 36 is just 6
1. '±' means 'plus or minus'
2. So 'plus or minus 6i' means that we have two possible answers: positive 6i or negative 6i
3. 'i' is the imaginary unit and is equal to the square root of -1

Solve the quadratic equation x2 + 38 = 2 for x.