What are the solutions to the equation x(x-8)(x-4)^2=225 ?

The solutions to the equation x(x-8)(x-4)^2=225 are x=-1,x=9,x=4+3i,x=4-3i

Find the zeros of x(x-8)(x-4)^2=225

The zeros of x(x-8)(x-4)^2=225 are x=-1,x=9,x=4+3i,x=4-3i

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x (x - 8) (x - 4)^{2} = 225

x = - 1, x = 9, x = 4 + 3 i, x = 4 - 3 i

Solution steps

x (x - 8) (x - 4)^{2} = 225

Expand

x (x - 8) (x - 4)^{2} : x^{4} - 16 x^{3} + 80 x^{2} - 128 x

x^{4} - 16 x^{3} + 80 x^{2} - 128 x = 225

Move

225

to the left side

x^{4} - 16 x^{3} + 80 x^{2} - 128 x - 225 = 0

Factor

x^{4} - 16 x^{3} + 80 x^{2} - 128 x - 225 : (x + 1) (x - 9) (x^{2} - 8 x + 25)

(x + 1) (x - 9) (x^{2} - 8 x + 25) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 9 = 0 or x^{2} - 8 x + 25 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 9 = 0 : x = 9

Solve

x^{2} - 8 x + 25 = 0 : x = 4 + 3 i, x = 4 - 3 i

The solutions are

x = - 1, x = 9, x = 4 + 3 i, x = 4 - 3 i

z^{5} = - 2

4 x^{3} = 500

29750 = 2 x^{3} - 1500

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

800 = π r^{2} 2 r

What are the solutions to the equation x(x-8)(x-4)^2=225 ?
The solutions to the equation x(x-8)(x-4)^2=225 are x=-1,x=9,x=4+3i,x=4-3i
Find the zeros of x(x-8)(x-4)^2=225
The zeros of x(x-8)(x-4)^2=225 are x=-1,x=9,x=4+3i,x=4-3i