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

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.

u-25=0

Add 25 to both sides of the equation.

u=25

u=25

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

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

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