What are the solutions to the equation (x+2)(x+3)(x+8)(x+12)=54x^2 ?

The solutions to the equation (x+2)(x+3)(x+8)(x+12)=54x^2 are x=-2(-sqrt(19)+5),x=-2(sqrt(19)+5)

Find the zeros of (x+2)(x+3)(x+8)(x+12)=54x^2

The zeros of (x+2)(x+3)(x+8)(x+12)=54x^2 are x=-2(-sqrt(19)+5),x=-2(sqrt(19)+5)

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(x + 2) (x + 3) (x + 8) (x + 12) = 54 x^{2}

x = - 2 (- 19 + 5), x = - 2 (19 + 5)

Decimal Notation

x = - 1.28220 \dots, x = - 18.71779 \dots

Solution steps

(x + 2) (x + 3) (x + 8) (x + 12) = 54 x^{2}

Expand

(x + 2) (x + 3) (x + 8) (x + 12) : x^{4} + 25 x^{3} + 202 x^{2} + 600 x + 576

x^{4} + 25 x^{3} + 202 x^{2} + 600 x + 576 = 54 x^{2}

Move

54 x^{2}

to the left side

x^{4} + 25 x^{3} + 148 x^{2} + 600 x + 576 = 0

Find one solution for

x^{4} + 25 x^{3} + 148 x^{2} + 600 x + 576 = 0

using Newton-Raphson:

x \approx - 1.28220 \dots

Apply long division:

\frac{x ^{4} + 25 x ^{3} + 148 x ^{2} + 600 x + 576}{x + 1.28220 \dots} = x^{3} + 23.71779 \dots x^{2} + 117.58898 \dots x + 449.22714 \dots

x^{3} + 23.71779 \dots x^{2} + 117.58898 \dots x + 449.22714 \dots \approx 0

Find one solution for

x^{3} + 23.71779 \dots x^{2} + 117.58898 \dots x + 449.22714 \dots = 0

using Newton-Raphson:

x \approx - 18.71779 \dots

Apply long division:

\frac{x ^{3} + 23.71779 \dots x ^{2} + 117.58898 \dots x + 449.22714 \dots}{x + 18.71779 \dots} = x^{2} + 5 x + 24

x^{2} + 5 x + 24 \approx 0

Find one solution for

x^{2} + 5 x + 24 = 0

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx - 1.28220 \dots : x = - 2 (- 19 + 5)

x \approx - 18.71779 \dots : x = - 2 (19 + 5)

x = - 2 (- 19 + 5), x = - 2 (19 + 5)

The solutions are

x = - 2 (- 19 + 5), x = - 2 (19 + 5)

8 x^{3} + 64 x^{2} + 120 x = 0

c^{3} - 8 = 0

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

v^{4} - 0.8949 v^{2} + 0.028367 = 0

x, x^{3} + 5 y = 25

What are the solutions to the equation (x+2)(x+3)(x+8)(x+12)=54x^2 ?
The solutions to the equation (x+2)(x+3)(x+8)(x+12)=54x^2 are x=-2(-sqrt(19)+5),x=-2(sqrt(19)+5)
Find the zeros of (x+2)(x+3)(x+8)(x+12)=54x^2
The zeros of (x+2)(x+3)(x+8)(x+12)=54x^2 are x=-2(-sqrt(19)+5),x=-2(sqrt(19)+5)