What are the solutions to the equation 3x^3+25=x^2+75x ?

The solutions to the equation 3x^3+25=x^2+75x are x= 1/3 ,x=-5,x=5

Find the zeros of 3x^3+25=x^2+75x

The zeros of 3x^3+25=x^2+75x are x= 1/3 ,x=-5,x=5

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3 x^{3} + 25 = x^{2} + 75 x

x = \frac{1}{3}, x = - 5, x = 5

Decimal Notation

x = 0.33333 \dots, x = - 5, x = 5

Solution steps

3 x^{3} + 25 = x^{2} + 75 x

Move

75 x

to the left side

3 x^{3} + 25 - 75 x = x^{2}

Move

x^{2}

to the left side

3 x^{3} + 25 - 75 x - x^{2} = 0

Write in the standard form

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

3 x^{3} - x^{2} - 75 x + 25 = 0

Factor

3 x^{3} - x^{2} - 75 x + 25 : (3 x - 1) (x + 5) (x - 5)

(3 x - 1) (x + 5) (x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x - 1 = 0 or x + 5 = 0 or x - 5 = 0

Solve

3 x - 1 = 0 : x = \frac{1}{3}

Solve

x + 5 = 0 : x = - 5

Solve

x - 5 = 0 : x = 5

The solutions are

x = \frac{1}{3}, x = - 5, x = 5

x^{5} + 32 = 0

(x - 3) (x + 2) (x - 1) = 0

y^{4} = 0

x, 4 x^{3} - 16 x = 0

2 x (x^{2} - 3) (x^{2} + 49) = 0

What are the solutions to the equation 3x^3+25=x^2+75x ?
The solutions to the equation 3x^3+25=x^2+75x are x= 1/3 ,x=-5,x=5
Find the zeros of 3x^3+25=x^2+75x
The zeros of 3x^3+25=x^2+75x are x= 1/3 ,x=-5,x=5