What are the solutions to the equation 36x^4+29x^2-7=0 ?

The solutions to the equation 36x^4+29x^2-7=0 are x=(sqrt(7))/6 ,x=-(sqrt(7))/6 ,x=i,x=-i

Find the zeros of 36x^4+29x^2-7=0

The zeros of 36x^4+29x^2-7=0 are x=(sqrt(7))/6 ,x=-(sqrt(7))/6 ,x=i,x=-i

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36 x^{4} + 29 x^{2} - 7 = 0

x = \frac{7}{6}, x = - \frac{7}{6}, x = i, x = - i

Solution steps

36 x^{4} + 29 x^{2} - 7 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

36 u^{2} + 29 u - 7 = 0

Solve

36 u^{2} + 29 u - 7 = 0 : u = \frac{7}{36}, u = - 1

u = \frac{7}{36}, u = - 1

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{7}{36} : x = \frac{7}{6}, x = - \frac{7}{6}

Solve

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

The solutions are

x = \frac{7}{6}, x = - \frac{7}{6}, x = i, x = - i

4 x^{3} + 16 x^{2} = 16 x + 64

x^{3} - 6 x^{2} - 36 x - 40 = 0

w (w - 6)^{2} = 0

x^{3} - 6 x^{2} + 9 x - 4 = 0

a^{6} - 5 = 9

What are the solutions to the equation 36x^4+29x^2-7=0 ?
The solutions to the equation 36x^4+29x^2-7=0 are x=(sqrt(7))/6 ,x=-(sqrt(7))/6 ,x=i,x=-i
Find the zeros of 36x^4+29x^2-7=0
The zeros of 36x^4+29x^2-7=0 are x=(sqrt(7))/6 ,x=-(sqrt(7))/6 ,x=i,x=-i