What are the solutions to the equation (x+3)^4+2(x+3)^2-8=0 ?

The solutions to the equation (x+3)^4+2(x+3)^2-8=0 are x=sqrt(2)-3,x=-sqrt(2)-3

Find the zeros of (x+3)^4+2(x+3)^2-8=0

The zeros of (x+3)^4+2(x+3)^2-8=0 are x=sqrt(2)-3,x=-sqrt(2)-3

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(x + 3)^{4} + 2 (x + 3)^{2} - 8 = 0

x = 2 - 3, x = - 2 - 3

Decimal Notation

x = - 1.58578 \dots, x = - 4.41421 \dots

Solution steps

(x + 3)^{4} + 2 (x + 3)^{2} - 8 = 0

Expand

(x + 3)^{4} + 2 (x + 3)^{2} - 8 : x^{4} + 12 x^{3} + 56 x^{2} + 120 x + 91

x^{4} + 12 x^{3} + 56 x^{2} + 120 x + 91 = 0

Find one solution for

x^{4} + 12 x^{3} + 56 x^{2} + 120 x + 91 = 0

using Newton-Raphson:

x \approx - 1.58578 \dots

Apply long division:

\frac{x ^{4} + 12 x ^{3} + 56 x ^{2} + 120 x + 91}{x + 1.58578 \dots} = x^{3} + 10.41421 \dots x^{2} + 39.48528 \dots x + 57.38477 \dots

x^{3} + 10.41421 \dots x^{2} + 39.48528 \dots x + 57.38477 \dots \approx 0

Find one solution for

x^{3} + 10.41421 \dots x^{2} + 39.48528 \dots x + 57.38477 \dots = 0

using Newton-Raphson:

x \approx - 4.41421 \dots

Apply long division:

\frac{x ^{3} + 10.41421 \dots x ^{2} + 39.48528 \dots x + 57.38477 \dots}{x + 4.41421 \dots} = x^{2} + 6 x + 13

x^{2} + 6 x + 13 \approx 0

Find one solution for

x^{2} + 6 x + 13 = 0

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx - 1.58578 \dots : x = 2 - 3

x \approx - 4.41421 \dots : x = - 2 - 3

x = 2 - 3, x = - 2 - 3

The solutions are

x = 2 - 3, x = - 2 - 3

x^{3} + 3 x^{2} - 112 = 0

x^{4} - \frac{6}{7} x^{2} + \frac{3}{35} = 0

x^{4} + x^{3} - x^{2} - 2 x - 2 = 0

5 x^{4} + 7 x^{2} - 12 = 0

x^{3} - 4 x - x^{2} + 4 = 0

What are the solutions to the equation (x+3)^4+2(x+3)^2-8=0 ?
The solutions to the equation (x+3)^4+2(x+3)^2-8=0 are x=sqrt(2)-3,x=-sqrt(2)-3
Find the zeros of (x+3)^4+2(x+3)^2-8=0
The zeros of (x+3)^4+2(x+3)^2-8=0 are x=sqrt(2)-3,x=-sqrt(2)-3