What are the solutions to the equation x^2(x^2-16)-49(x^2-16)=0 ?

The solutions to the equation x^2(x^2-16)-49(x^2-16)=0 are x=7,x=-7,x=4,x=-4

Find the zeros of x^2(x^2-16)-49(x^2-16)=0

The zeros of x^2(x^2-16)-49(x^2-16)=0 are x=7,x=-7,x=4,x=-4

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x^{2} (x^{2} - 16) - 49 (x^{2} - 16) = 0

x = 7, x = - 7, x = 4, x = - 4

Solution steps

x^{2} (x^{2} - 16) - 49 (x^{2} - 16) = 0

Expand

x^{2} (x^{2} - 16) - 49 (x^{2} - 16) : x^{4} - 65 x^{2} + 784

x^{4} - 65 x^{2} + 784 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 65 u + 784 = 0

Solve

u^{2} - 65 u + 784 = 0 : u = 49, u = 16

u = 49, u = 16

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 49 : x = 7, x = - 7

Solve

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

The solutions are

x = 7, x = - 7, x = 4, x = - 4

v^{8} v + 4 v - 14 = - 53

(2 x - 8)^{8} = x^{8}

2 x^{3} + 16 x^{2} + 30 x = 0

x^{6} - x^{3} - 6 = 0

y^{4} + 4 y^{2} - 5 = 0

What are the solutions to the equation x^2(x^2-16)-49(x^2-16)=0 ?
The solutions to the equation x^2(x^2-16)-49(x^2-16)=0 are x=7,x=-7,x=4,x=-4
Find the zeros of x^2(x^2-16)-49(x^2-16)=0
The zeros of x^2(x^2-16)-49(x^2-16)=0 are x=7,x=-7,x=4,x=-4