What are the solutions to the equation -5x^2=36-x^4 ?

The solutions to the equation -5x^2=36-x^4 are x=2i,x=-2i,x=3,x=-3

Find the zeros of -5x^2=36-x^4

The zeros of -5x^2=36-x^4 are x=2i,x=-2i,x=3,x=-3

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- 5 x^{2} = 36 - x^{4}

x = 2 i, x = - 2 i, x = 3, x = - 3

Solution steps

- 5 x^{2} = 36 - x^{4}

Switch sides

36 - x^{4} = - 5 x^{2}

Move

5 x^{2}

to the left side

36 - x^{4} + 5 x^{2} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- x^{4} + 5 x^{2} + 36 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

- u^{2} + 5 u + 36 = 0

Solve

- u^{2} + 5 u + 36 = 0 : u = - 4, u = 9

u = - 4, u = 9

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = - 4 : x = 2 i, x = - 2 i

Solve

x^{2} = 9 : x = 3, x = - 3

The solutions are

x = 2 i, x = - 2 i, x = 3, x = - 3

x^{3} - 15 x - 1 = 0

2 + 3 x^{2} - x^{3}

(x^{2} + 1)^{2} - 2 x^{2} = 0

x^{6} - 64

x (x + 6) (x + 2) = 64

What are the solutions to the equation -5x^2=36-x^4 ?
The solutions to the equation -5x^2=36-x^4 are x=2i,x=-2i,x=3,x=-3
Find the zeros of -5x^2=36-x^4
The zeros of -5x^2=36-x^4 are x=2i,x=-2i,x=3,x=-3