What are the solutions to the equation x^3+x^2=((11x+10))/3 ?

The solutions to the equation x^3+x^2=((11x+10))/3 are x=-2,x=(3+sqrt(69))/6 ,x=(3-sqrt(69))/6

Find the zeros of x^3+x^2=((11x+10))/3

The zeros of x^3+x^2=((11x+10))/3 are x=-2,x=(3+sqrt(69))/6 ,x=(3-sqrt(69))/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{3} + x^{2} = \frac{( 11 x + 10 )}{3}

x = - 2, x = \frac{3 + 69}{6}, x = \frac{3 - 69}{6}

Decimal Notation

x = - 2, x = 1.88443 \dots, x = - 0.88443 \dots

Solution steps

x^{3} + x^{2} = \frac{( 11 x + 10 )}{3}

Multiply both sides by

3

3 x^{3} + 3 x^{2} = 11 x + 10

Move

10

to the left side

3 x^{3} + 3 x^{2} - 10 = 11 x

Move

11 x

to the left side

3 x^{3} + 3 x^{2} - 10 - 11 x = 0

Write in the standard form

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

3 x^{3} + 3 x^{2} - 11 x - 10 = 0

Factor

3 x^{3} + 3 x^{2} - 11 x - 10 : (x + 2) (3 x^{2} - 3 x - 5)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 2 = 0 : x = - 2

Solve

3 x^{2} - 3 x - 5 = 0 : x = \frac{3 + 69}{6}, x = \frac{3 - 69}{6}

The solutions are

x = - 2, x = \frac{3 + 69}{6}, x = \frac{3 - 69}{6}

x^{4} + x^{2} = 1

r^{3} - 7 r^{2} - 7 r - 8 = 0

- x^{3} + x^{2} + 21 x - 45 = 0

\frac{x ^{5}}{4 + 5} = 13

x^{4} - 8 x^{2} + 4 = 0

What are the solutions to the equation x^3+x^2=((11x+10))/3 ?
The solutions to the equation x^3+x^2=((11x+10))/3 are x=-2,x=(3+sqrt(69))/6 ,x=(3-sqrt(69))/6
Find the zeros of x^3+x^2=((11x+10))/3
The zeros of x^3+x^2=((11x+10))/3 are x=-2,x=(3+sqrt(69))/6 ,x=(3-sqrt(69))/6