What are the solutions to the equation x^4+8=-9x^2 ?

The solutions to the equation x^4+8=-9x^2 are x=i,x=-i,x=2sqrt(2)i,x=-2sqrt(2)i

Find the zeros of x^4+8=-9x^2

The zeros of x^4+8=-9x^2 are x=i,x=-i,x=2sqrt(2)i,x=-2sqrt(2)i

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x^{4} + 8 = - 9 x^{2}

x = i, x = - i, x = 22 i, x = - 22 i

Solution steps

x^{4} + 8 = - 9 x^{2}

Move

9 x^{2}

to the left side

x^{4} + 8 + 9 x^{2} = 0

Write in the standard form

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

x^{4} + 9 x^{2} + 8 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} + 9 u + 8 = 0

Solve

u^{2} + 9 u + 8 = 0 : u = - 1, u = - 8

u = - 1, u = - 8

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = - 1 : x = i, x = - i

Solve

x^{2} = - 8 : x = 22 i, x = - 22 i

The solutions are

x = i, x = - i, x = 22 i, x = - 22 i

x^{3} + 5 x^{2} + 7 x + 3 = 0

12 x^{4} - 32 x^{3} + 13 x^{2} + 8 x + 1 = 0

a^{3} = 3^{9} \times 1 2^{3} \times 2 1^{6}

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

y, 2 x^{3} y^{1} = y (2 x^{2} - y^{2})

What are the solutions to the equation x^4+8=-9x^2 ?
The solutions to the equation x^4+8=-9x^2 are x=i,x=-i,x=2sqrt(2)i,x=-2sqrt(2)i
Find the zeros of x^4+8=-9x^2
The zeros of x^4+8=-9x^2 are x=i,x=-i,x=2sqrt(2)i,x=-2sqrt(2)i