# Solve for a a^4-14a^2+45=0

Substitute into the equation. This will make the quadratic formula easy to use.
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 .
Add to both sides of the equation.
The final solution is all the values that make true.
Substitute the real value of back into the solved equation.
Solve the first equation for .
Solve the equation for .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Solve the second equation for .
Solve the equation for .
Take the 1th root of each side of the equation to set up the solution for
Remove the perfect root factor under the radical to solve for .
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Evaluate as .
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
The solution to is .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for a a^4-14a^2+45=0

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