What are the solutions to the equation (x^2+3)^2-19(x^2+3)+84=0 ?

The solutions to the equation (x^2+3)^2-19(x^2+3)+84=0 are x=3,x=-3,x=2,x=-2

Find the zeros of (x^2+3)^2-19(x^2+3)+84=0

The zeros of (x^2+3)^2-19(x^2+3)+84=0 are x=3,x=-3,x=2,x=-2

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(x^{2} + 3)^{2} - 19 (x^{2} + 3) + 84 = 0

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

Solution steps

(x^{2} + 3)^{2} - 19 (x^{2} + 3) + 84 = 0

Expand

(x^{2} + 3)^{2} - 19 (x^{2} + 3) + 84 : x^{4} - 13 x^{2} + 36

x^{4} - 13 x^{2} + 36 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 13 u + 36 = 0

Solve

u^{2} - 13 u + 36 = 0 : u = 9, u = 4

u = 9, u = 4

Substitute back

u = x^{2},

solve for

x

Solve

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

Solve

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

The solutions are

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

x^{9} + 2 x^{8} + 4 x^{7} + 8 x^{6} + 16 x^{5} + 32 x^{4} + 64 x^{3} + 128 x^{2} + 256 x + 512 = 0

m^{3} - 2 m^{2} - 4 m + 8 = 0

x^{3} = \frac{- 7}{2}

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

3 x^{3} + x - 10 = 0

What are the solutions to the equation (x^2+3)^2-19(x^2+3)+84=0 ?
The solutions to the equation (x^2+3)^2-19(x^2+3)+84=0 are x=3,x=-3,x=2,x=-2
Find the zeros of (x^2+3)^2-19(x^2+3)+84=0
The zeros of (x^2+3)^2-19(x^2+3)+84=0 are x=3,x=-3,x=2,x=-2