What are the solutions to the equation x^2(x+3)^2=176 ?

The solutions to the equation x^2(x+3)^2=176 are x\approx 2.43909…,x\approx-5.43909…

Find the zeros of x^2(x+3)^2=176

The zeros of x^2(x+3)^2=176 are x\approx 2.43909…,x\approx-5.43909…

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x^{2} (x + 3)^{2} = 176

x \approx 2.43909 \dots, x \approx - 5.43909 \dots

Solution steps

x^{2} (x + 3)^{2} = 176

Expand

x^{2} (x + 3)^{2} : x^{4} + 6 x^{3} + 9 x^{2}

x^{4} + 6 x^{3} + 9 x^{2} = 176

Move

176

to the left side

x^{4} + 6 x^{3} + 9 x^{2} - 176 = 0

Find one solution for

x^{4} + 6 x^{3} + 9 x^{2} - 176 = 0

using Newton-Raphson:

x \approx 2.43909 \dots

Apply long division:

\frac{x ^{4} + 6 x ^{3} + 9 x ^{2} - 176}{x - 2.43909 \dots} = x^{3} + 8.43909 \dots x^{2} + 29.58379 \dots x + 72.15779 \dots

x^{3} + 8.43909 \dots x^{2} + 29.58379 \dots x + 72.15779 \dots \approx 0

Find one solution for

x^{3} + 8.43909 \dots x^{2} + 29.58379 \dots x + 72.15779 \dots = 0

using Newton-Raphson:

x \approx - 5.43909 \dots

Apply long division:

\frac{x ^{3} + 8.43909 \dots x ^{2} + 29.58379 \dots x + 72.15779 \dots}{x + 5.43909 \dots} = x^{2} + 3 x + 13.26649 \dots

x^{2} + 3 x + 13.26649 \dots \approx 0

Find one solution for

x^{2} + 3 x + 13.26649 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 2.43909 \dots, x \approx - 5.43909 \dots

2 x^{3} - 3 x^{2} + 5 x + 1 = 0

x, 9 x^{3} - 5 y^{2} = 7

1300000 = 480000 (1 + x)^{12}

x^{3} - x^{2} - 14 x + 24 = 0

8 y^{2} = - 15 - y^{4}

What are the solutions to the equation x^2(x+3)^2=176 ?
The solutions to the equation x^2(x+3)^2=176 are x\approx 2.43909…,x\approx-5.43909…
Find the zeros of x^2(x+3)^2=176
The zeros of x^2(x+3)^2=176 are x\approx 2.43909…,x\approx-5.43909…