y4-37y2+36=0

Substitute u=y2 into the equation. This will make the quadratic formula easy to use.

u2-37u+36=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 36 and whose sum is -37.

-36,-1

Write the factored form using these integers.

(u-36)(u-1)=0

(u-36)(u-1)=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-36=0

u-1=0

Set the first factor equal to 0.

u-36=0

Add 36 to both sides of the equation.

u=36

u=36

Set the next factor equal to 0.

u-1=0

Add 1 to both sides of the equation.

u=1

u=1

The final solution is all the values that make (u-36)(u-1)=0 true.

u=36,1

Substitute the real value of u=y2 back into the solved equation.

y2=36

(y2)1=1

Solve the first equation for y.

y2=36

Take the square root of both sides of the equation to eliminate the exponent on the left side.

y=±36

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite 36 as 62.

y=±62

Pull terms out from under the radical, assuming positive real numbers.

y=±6

y=±6

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=6

Next, use the negative value of the ± to find the second solution.

y=-6

The complete solution is the result of both the positive and negative portions of the solution.

y=6,-6

y=6,-6

y=6,-6

y=6,-6

Solve the second equation for y.

(y2)1=1

Take the 1th root of each side of the equation to set up the solution for y

(y2)1⋅11=11

Remove the perfect root factor y2 under the radical to solve for y.

y2=11

Take the square root of both sides of the equation to eliminate the exponent on the left side.

y=±11

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Any root of 1 is 1.

y=±1

Any root of 1 is 1.

y=±1

y=±1

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=1

Next, use the negative value of the ± to find the second solution.

y=-1

The complete solution is the result of both the positive and negative portions of the solution.

y=1,-1

y=1,-1

y=1,-1

y=1,-1

The solution to y4-37y2+36=0 is y=6,-6,1,-1.

y=6,-6,1,-1

Solve for y y^4-37y^2+36=0