What are the solutions to the equation (m^4+25m^2+25)-12m^2-60m-49=0 ?

The solutions to the equation (m^4+25m^2+25)-12m^2-60m-49=0 are m\approx-0.37002…,m\approx 3.04646…

Find the zeros of (m^4+25m^2+25)-12m^2-60m-49=0

The zeros of (m^4+25m^2+25)-12m^2-60m-49=0 are m\approx-0.37002…,m\approx 3.04646…

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(m^{4} + 25 m^{2} + 25) - 12 m^{2} - 60 m - 49 = 0

m \approx - 0.37002 \dots, m \approx 3.04646 \dots

Solution steps

(m^{4} + 25 m^{2} + 25) - 12 m^{2} - 60 m - 49 = 0

Refine

m^{4} + 13 m^{2} - 60 m - 24 = 0

Find one solution for

m^{4} + 13 m^{2} - 60 m - 24 = 0

using Newton-Raphson:

m \approx - 0.37002 \dots

Apply long division:

\frac{m ^{4} + 13 m ^{2} - 60 m - 24}{m + 0.37002 \dots} = m^{3} - 0.37002 \dots m^{2} + 13.13691 \dots m - 64.86095 \dots

m^{3} - 0.37002 \dots m^{2} + 13.13691 \dots m - 64.86095 \dots \approx 0

Find one solution for

m^{3} - 0.37002 \dots m^{2} + 13.13691 \dots m - 64.86095 \dots = 0

using Newton-Raphson:

m \approx 3.04646 \dots

Apply long division:

\frac{m ^{3} - 0.37002 \dots m ^{2} + 13.13691 \dots m - 64.86095 \dots}{m - 3.04646 \dots} = m^{2} + 2.67643 \dots m + 21.29058 \dots

m^{2} + 2.67643 \dots m + 21.29058 \dots \approx 0

Find one solution for

m^{2} + 2.67643 \dots m + 21.29058 \dots = 0

using Newton-Raphson:

No Solution for

m \in R

The solutions are

m \approx - 0.37002 \dots, m \approx 3.04646 \dots

x^{4} + 2 x^{3} - 8 x - 16 = 0

(3 x - 4)^{10} - 3 = 1021

(3 x^{4})^{5} = (3^{3})^{3}

3 \frac{x}{5} - \frac{1}{4} = x^{7} \frac{x}{10} - \frac{1}{5}

5 x^{4} + 2 x^{3} - 1 = 0

What are the solutions to the equation (m^4+25m^2+25)-12m^2-60m-49=0 ?
The solutions to the equation (m^4+25m^2+25)-12m^2-60m-49=0 are m\approx-0.37002…,m\approx 3.04646…
Find the zeros of (m^4+25m^2+25)-12m^2-60m-49=0
The zeros of (m^4+25m^2+25)-12m^2-60m-49=0 are m\approx-0.37002…,m\approx 3.04646…