# Evaluate n^(1/2)+6n^(1/4)-16=0

Evaluate n^(1/2)+6n^(1/4)-16=0
Factor the left side of the equation.
Rewrite as .
Let . Substitute for all occurrences of .
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.
Replace all occurrences of with .
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 .
Solve for .
Add to both sides of the equation.
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Simplify the exponent.
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.
Raise to the power of .
Set equal to and solve for .
Set equal to .
Solve for .
Subtract from both sides of the equation.
Raise each side of the equation to the power of to eliminate the fractional exponent on the left side.
Simplify the exponent.
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.
Raise to the power of .
The final solution is all the values that make true.
Exclude the solutions that do not make true.
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