# Solve for x |x^2-5x|=14

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.
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 the first factor equal to and solve.
Set the first factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
The final solution is all the values that make true.
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.
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 .
Subtract from .
Rewrite as .
Rewrite as .
Rewrite as .
Multiply by .
The final answer is the combination of both solutions.
The solution to the equation includes both the positive and negative portions of the solution.
Solve for x |x^2-5x|=14
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