What are the solutions to the equation x^3=x^2-7x+7 ?

The solutions to the equation x^3=x^2-7x+7 are x=1,x=sqrt(7)i,x=-sqrt(7)i

Find the zeros of x^3=x^2-7x+7

The zeros of x^3=x^2-7x+7 are x=1,x=sqrt(7)i,x=-sqrt(7)i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^{3} = x^{2} - 7 x + 7

x = 1, x = 7 i, x = - 7 i

Solution steps

x^{3} = x^{2} - 7 x + 7

Move

7

to the left side

x^{3} - 7 = x^{2} - 7 x

Move

7 x

to the left side

x^{3} - 7 + 7 x = x^{2}

Move

x^{2}

to the left side

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

Write in the standard form

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

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

Factor

x^{3} - x^{2} + 7 x - 7 : (x - 1) (x^{2} + 7)

(x - 1) (x^{2} + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + 7 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + 7 = 0 : x = 7 i, x = - 7 i

The solutions are

x = 1, x = 7 i, x = - 7 i

n^{3} + 2 n^{2} - 9 n - 18 = 0

z^{5} = 1 + i

x^{3} - 2 x^{2} + 5 x - 1 = 2

x^{4} + 8 x^{3} + 14 x^{2} - 17 x - 42 = 0

2 x^{6} + 300 = 30950

What are the solutions to the equation x^3=x^2-7x+7 ?
The solutions to the equation x^3=x^2-7x+7 are x=1,x=sqrt(7)i,x=-sqrt(7)i
Find the zeros of x^3=x^2-7x+7
The zeros of x^3=x^2-7x+7 are x=1,x=sqrt(7)i,x=-sqrt(7)i