# Find All Complex Solutions x-3 = square root of 19-3x

Find All Complex Solutions x-3 = square root of 19-3x
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
To remove the radical on the left side of the equation, square both sides of the equation.
Simplify each side of the equation.
Use to rewrite as .
Simplify the left side.
Simplify .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify.
Simplify the right side.
Simplify .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Multiply by .
Subtract from .
Solve for .
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
Subtract from both sides of the equation.
Subtract from .
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Set equal to .
Add to both sides of the equation.
Set equal to and solve for .
Set equal to .
Subtract from both sides of the equation.
The final solution is all the values that make true.
Exclude the solutions that do not make true.
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