What are the solutions to the equation (x+5)^3=-27 ?

The solutions to the equation (x+5)^3=-27 are x=-8,x=-7/2+i(3sqrt(3))/2 ,x=-7/2-i(3sqrt(3))/2

Find the zeros of (x+5)^3=-27

The zeros of (x+5)^3=-27 are x=-8,x=-7/2+i(3sqrt(3))/2 ,x=-7/2-i(3sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x + 5)^{3} = - 27

x = - 8, x = - \frac{7}{2} + i \frac{3 3}{2}, x = - \frac{7}{2} - i \frac{3 3}{2}

Solution steps

(x + 5)^{3} = - 27

Expand

(x + 5)^{3} : x^{3} + 15 x^{2} + 75 x + 125

x^{3} + 15 x^{2} + 75 x + 125 = - 27

Move

27

to the left side

x^{3} + 15 x^{2} + 75 x + 152 = 0

Factor

x^{3} + 15 x^{2} + 75 x + 152 : (x + 8) (x^{2} + 7 x + 19)

(x + 8) (x^{2} + 7 x + 19) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 8 = 0 or x^{2} + 7 x + 19 = 0

Solve

x + 8 = 0 : x = - 8

Solve

x^{2} + 7 x + 19 = 0 : x = - \frac{7}{2} + i \frac{3 3}{2}, x = - \frac{7}{2} - i \frac{3 3}{2}

The solutions are

x = - 8, x = - \frac{7}{2} + i \frac{3 3}{2}, x = - \frac{7}{2} - i \frac{3 3}{2}

x^{3} - 24 x = 5 x^{2}

36 k^{3} + 48 k^{2} - 84 k - 112 = 0

r^{3} + 12 r^{2} - 60 r + 64 = 0

x, y^{4} = C x^{3} + 2

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

What are the solutions to the equation (x+5)^3=-27 ?
The solutions to the equation (x+5)^3=-27 are x=-8,x=-7/2+i(3sqrt(3))/2 ,x=-7/2-i(3sqrt(3))/2
Find the zeros of (x+5)^3=-27
The zeros of (x+5)^3=-27 are x=-8,x=-7/2+i(3sqrt(3))/2 ,x=-7/2-i(3sqrt(3))/2