# Solve for y y^4-29y^2+100=0

y4-29y2+100=0
Substitute u=y2 into the equation. This will make the quadratic formula easy to use.
u2-29u+100=0
u=y2
Factor u2-29u+100 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 100 and whose sum is -29.
-25,-4
Write the factored form using these integers.
(u-25)(u-4)=0
(u-25)(u-4)=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-25=0
u-4=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
u-25=0
Add 25 to both sides of the equation.
u=25
u=25
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
u-4=0
Add 4 to both sides of the equation.
u=4
u=4
The final solution is all the values that make (u-25)(u-4)=0 true.
u=25,4
Substitute the real value of u=y2 back into the solved equation.
y2=25
(y2)1=4
Solve the first equation for y.
y2=25
Solve the equation for y.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±25
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite 25 as 52.
y=±52
Pull terms out from under the radical, assuming positive real numbers.
y=±5
y=±5
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.
y=5
Next, use the negative value of the ± to find the second solution.
y=-5
The complete solution is the result of both the positive and negative portions of the solution.
y=5,-5
y=5,-5
y=5,-5
y=5,-5
Solve the second equation for y.
(y2)1=4
Solve the equation for y.
Take the 1th root of each side of the equation to set up the solution for y
(y2)1⋅11=41
Remove the perfect root factor y2 under the radical to solve for y.
y2=41
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±41
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Evaluate 41 as 4.
y=±4
Rewrite 4 as 22.
y=±22
Pull terms out from under the radical, assuming positive real numbers.
y=±2
y=±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.
y=2
Next, use the negative value of the ± to find the second solution.
y=-2
The complete solution is the result of both the positive and negative portions of the solution.
y=2,-2
y=2,-2
y=2,-2
y=2,-2
The solution to y4-29y2+100=0 is y=5,-5,2,-2.
y=5,-5,2,-2
Solve for y y^4-29y^2+100=0

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