What are the solutions to the equation 500=4x^3-80x^2+400x ?

The solutions to the equation 500=4x^3-80x^2+400x are x=5,x=(15+5sqrt(5))/2 ,x=(15-5sqrt(5))/2

Find the zeros of 500=4x^3-80x^2+400x

The zeros of 500=4x^3-80x^2+400x are x=5,x=(15+5sqrt(5))/2 ,x=(15-5sqrt(5))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

500 = 4 x^{3} - 80 x^{2} + 400 x

x = 5, x = \frac{15 + 5 5}{2}, x = \frac{15 - 5 5}{2}

Decimal Notation

x = 5, x = 13.09016 \dots, x = 1.90983 \dots

Solution steps

500 = 4 x^{3} - 80 x^{2} + 400 x

Switch sides

4 x^{3} - 80 x^{2} + 400 x = 500

Move

500

to the left side

4 x^{3} - 80 x^{2} + 400 x - 500 = 0

Factor

4 x^{3} - 80 x^{2} + 400 x - 500 : 4 (x - 5) (x^{2} - 15 x + 25)

4 (x - 5) (x^{2} - 15 x + 25) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 5 = 0 or x^{2} - 15 x + 25 = 0

Solve

x - 5 = 0 : x = 5

Solve

x^{2} - 15 x + 25 = 0 : x = \frac{15 + 5 5}{2}, x = \frac{15 - 5 5}{2}

The solutions are

x = 5, x = \frac{15 + 5 5}{2}, x = \frac{15 - 5 5}{2}

y^{3} + y^{2} = 4 y + 4

- 800 x^{3} + 150 x^{2} + 300 x + 600 = 0

4 x^{3} - 24 x^{2} + 44 x - 24 = 0

x^{3} - 4 x^{2} - 6 x + 7 = 0

x^{4} + 2 = 0

What are the solutions to the equation 500=4x^3-80x^2+400x ?
The solutions to the equation 500=4x^3-80x^2+400x are x=5,x=(15+5sqrt(5))/2 ,x=(15-5sqrt(5))/2
Find the zeros of 500=4x^3-80x^2+400x
The zeros of 500=4x^3-80x^2+400x are x=5,x=(15+5sqrt(5))/2 ,x=(15-5sqrt(5))/2