What are the solutions to the equation x^2(x^2-16)-25(x^2-16)=0 ?

The solutions to the equation x^2(x^2-16)-25(x^2-16)=0 are x=5,x=-5,x=4,x=-4

Find the zeros of x^2(x^2-16)-25(x^2-16)=0

The zeros of x^2(x^2-16)-25(x^2-16)=0 are x=5,x=-5,x=4,x=-4

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x^{2} (x^{2} - 16) - 25 (x^{2} - 16) = 0

x = 5, x = - 5, x = 4, x = - 4

Solution steps

x^{2} (x^{2} - 16) - 25 (x^{2} - 16) = 0

Expand

x^{2} (x^{2} - 16) - 25 (x^{2} - 16) : x^{4} - 41 x^{2} + 400

x^{4} - 41 x^{2} + 400 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 41 u + 400 = 0

Solve

u^{2} - 41 u + 400 = 0 : u = 25, u = 16

u = 25, u = 16

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 25 : x = 5, x = - 5

Solve

x^{2} = 16 : x = 4, x = - 4

The solutions are

x = 5, x = - 5, x = 4, x = - 4

x^{3} + x^{2} + x + 6 = 0

x^{5} = x^{3}

5 x^{2} + 2 x^{3} = 441

D^{3} - 11 D - 20 = 0

19 - x^{2} x = - 5

What are the solutions to the equation x^2(x^2-16)-25(x^2-16)=0 ?
The solutions to the equation x^2(x^2-16)-25(x^2-16)=0 are x=5,x=-5,x=4,x=-4
Find the zeros of x^2(x^2-16)-25(x^2-16)=0
The zeros of x^2(x^2-16)-25(x^2-16)=0 are x=5,x=-5,x=4,x=-4