# Solve for a a^4-9a^2+14=0 a4-9a2+14=0
Substitute u=a2 into the equation. This will make the quadratic formula easy to use.
u2-9u+14=0
u=a2
Factor u2-9u+14 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 14 and whose sum is -9.
-7,-2
Write the factored form using these integers.
(u-7)(u-2)=0
(u-7)(u-2)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
u-7=0
u-2=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
u-7=0
Add 7 to both sides of the equation.
u=7
u=7
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
u-2=0
Add 2 to both sides of the equation.
u=2
u=2
The final solution is all the values that make (u-7)(u-2)=0 true.
u=7,2
Substitute the real value of u=a2 back into the solved equation.
a2=7
(a2)1=2
Solve the first equation for a.
a2=7
Solve the equation for a.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
a=±7
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.
a=7
Next, use the negative value of the ± to find the second solution.
a=-7
The complete solution is the result of both the positive and negative portions of the solution.
a=7,-7
a=7,-7
a=7,-7
Solve the second equation for a.
(a2)1=2
Solve the equation for a.
Take the 1th root of each side of the equation to set up the solution for a
(a2)1⋅11=21
Remove the perfect root factor a2 under the radical to solve for a.
a2=21
Take the square root of both sides of the equation to eliminate the exponent on the left side.
a=±21
The complete solution is the result of both the positive and negative portions of the solution.
Evaluate 21 as 2.
a=±2
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.
a=2
Next, use the negative value of the ± to find the second solution.
a=-2
The complete solution is the result of both the positive and negative portions of the solution.
a=2,-2
a=2,-2
a=2,-2
a=2,-2
The solution to a4-9a2+14=0 is a=7,-7,2,-2.
a=7,-7,2,-2
The result can be shown in multiple forms.
Exact Form:
a=7,-7,2,-2
Decimal Form:
a=2.64575131…,-2.64575131…,1.41421356…,-1.41421356…
Solve for a a^4-9a^2+14=0

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