# Solve for x |x^2-4x|=4 Remove the absolute value term. This creates a on the right side of the equation because .
Set up the positive portion of the solution.
Solve the first equation for .
Move to the left side of the equation by subtracting it from both sides.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
Simplify the numerator.
Raise to the power of .
Multiply by .
Multiply by .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Multiply by .
Simplify .
The final answer is the combination of both solutions.
Set up the negative portion of the solution.
Solve the second equation for .
Move to the left side of the equation by adding it to both sides.
Factor using the perfect square rule.
Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
Set equal to and solve for .
Set the factor equal to .
Add to both sides of the equation.
The solution is the result of .
The solution to the equation includes both the positive and negative portions of the solution.
Exclude the solutions that do not make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for x |x^2-4x|=4     