What are the solutions to the equation (x^2+5x+25)(x-5)-5=86 ?

The solutions to the equation (x^2+5x+25)(x-5)-5=86 are x=6,x=-3+3sqrt(3)i,x=-3-3sqrt(3)i

Find the zeros of (x^2+5x+25)(x-5)-5=86

The zeros of (x^2+5x+25)(x-5)-5=86 are x=6,x=-3+3sqrt(3)i,x=-3-3sqrt(3)i

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(x^{2} + 5 x + 25) (x - 5) - 5 = 86

x = 6, x = - 3 + 33 i, x = - 3 - 33 i

Solution steps

(x^{2} + 5 x + 25) (x - 5) - 5 = 86

Expand

(x^{2} + 5 x + 25) (x - 5) - 5 : x^{3} - 130

x^{3} - 130 = 86

Move

86

to the left side

x^{3} - 216 = 0

Factor

x^{3} - 216 : (x - 6) (x^{2} + 6 x + 36)

(x - 6) (x^{2} + 6 x + 36) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 6 = 0 or x^{2} + 6 x + 36 = 0

Solve

x - 6 = 0 : x = 6

Solve

x^{2} + 6 x + 36 = 0 : x = - 3 + 33 i, x = - 3 - 33 i

The solutions are

x = 6, x = - 3 + 33 i, x = - 3 - 33 i

x^{5} + 4 x + 1 = 0

z^{87} = 0

12 x^{4} - 4 x^{2} - 1 = 0

2 - x = x^{3}

(x^{2} - 6) (x^{2} + 1) = 0

What are the solutions to the equation (x^2+5x+25)(x-5)-5=86 ?
The solutions to the equation (x^2+5x+25)(x-5)-5=86 are x=6,x=-3+3sqrt(3)i,x=-3-3sqrt(3)i
Find the zeros of (x^2+5x+25)(x-5)-5=86
The zeros of (x^2+5x+25)(x-5)-5=86 are x=6,x=-3+3sqrt(3)i,x=-3-3sqrt(3)i