What are the solutions to the equation 500x-500x^3=96 ?

The solutions to the equation 500x-500x^3=96 are x= 1/5 ,x=(-1+sqrt(97))/(10),x=-(1+sqrt(97))/(10)

Find the zeros of 500x-500x^3=96

The zeros of 500x-500x^3=96 are x= 1/5 ,x=(-1+sqrt(97))/(10),x=-(1+sqrt(97))/(10)

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500 x - 500 x^{3} = 96

x = \frac{1}{5}, x = \frac{- 1 + 97}{10}, x = - \frac{1 + 97}{10}

Decimal Notation

x = 0.2, x = 0.88488 \dots, x = - 1.08488 \dots

Solution steps

500 x - 500 x^{3} = 96

Move

96

to the left side

500 x - 500 x^{3} - 96 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 500 x^{3} + 500 x - 96 = 0

Factor

- 500 x^{3} + 500 x - 96 : - 4 (5 x - 1) (25 x^{2} + 5 x - 24)

- 4 (5 x - 1) (25 x^{2} + 5 x - 24) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5 x - 1 = 0 or 25 x^{2} + 5 x - 24 = 0

Solve

5 x - 1 = 0 : x = \frac{1}{5}

Solve

25 x^{2} + 5 x - 24 = 0 : x = \frac{- 1 + 97}{10}, x = - \frac{1 + 97}{10}

The solutions are

x = \frac{1}{5}, x = \frac{- 1 + 97}{10}, x = - \frac{1 + 97}{10}

2 x^{3} + 5 x^{2} - 36 x = 90

x, y^{3} - x^{3} = 3

b^{3} = 5

x = x - x^{3} - 4 \cdot x^{2} + 10

0 = x (x + 5) (x^{2} - 8 x - 19)

What are the solutions to the equation 500x-500x^3=96 ?
The solutions to the equation 500x-500x^3=96 are x= 1/5 ,x=(-1+sqrt(97))/(10),x=-(1+sqrt(97))/(10)
Find the zeros of 500x-500x^3=96
The zeros of 500x-500x^3=96 are x= 1/5 ,x=(-1+sqrt(97))/(10),x=-(1+sqrt(97))/(10)