What are the solutions to the equation -(12x^5-8x^3)=25x^2 ?

The solutions to the equation -(12x^5-8x^3)=25x^2 are x=0,x\approx-1.45024…

Find the zeros of -(12x^5-8x^3)=25x^2

The zeros of -(12x^5-8x^3)=25x^2 are x=0,x\approx-1.45024…

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- (12 x^{5} - 8 x^{3}) = 25 x^{2}

x = 0, x \approx - 1.45024 \dots

Solution steps

- (12 x^{5} - 8 x^{3}) = 25 x^{2}

Expand

- (12 x^{5} - 8 x^{3}) : - 12 x^{5} + 8 x^{3}

- 12 x^{5} + 8 x^{3} = 25 x^{2}

Move

25 x^{2}

to the left side

- 12 x^{5} + 8 x^{3} - 25 x^{2} = 0

Factor

- 12 x^{5} + 8 x^{3} - 25 x^{2} : - x^{2} (12 x^{3} - 8 x + 25)

- x^{2} (12 x^{3} - 8 x + 25) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 12 x^{3} - 8 x + 25 = 0

Solve

12 x^{3} - 8 x + 25 = 0 : x \approx - 1.45024 \dots

The solutions are

x = 0, x \approx - 1.45024 \dots

a, a^{3} + b^{3} = c^{3} + d^{3}

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

(x + 1)^{3} = (x + 1)^{2}

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

14 x^{3} + x = x^{2}

What are the solutions to the equation -(12x^5-8x^3)=25x^2 ?
The solutions to the equation -(12x^5-8x^3)=25x^2 are x=0,x\approx-1.45024…
Find the zeros of -(12x^5-8x^3)=25x^2
The zeros of -(12x^5-8x^3)=25x^2 are x=0,x\approx-1.45024…