What are the solutions to the equation 4.5t^4+3.2t^3+25t=20 ?

The solutions to the equation 4.5t^4+3.2t^3+25t=20 are t\approx 0.70892…,t\approx-2.22962…

Find the zeros of 4.5t^4+3.2t^3+25t=20

The zeros of 4.5t^4+3.2t^3+25t=20 are t\approx 0.70892…,t\approx-2.22962…

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4.5 t^{4} + 3.2 t^{3} + 25 t = 20

t \approx 0.70892 \dots, t \approx - 2.22962 \dots

Solution steps

4.5 t^{4} + 3.2 t^{3} + 25 t = 20

Multiply both sides by

10

45 t^{4} + 32 t^{3} + 250 t = 200

Move

200

to the left side

45 t^{4} + 32 t^{3} + 250 t - 200 = 0

Find one solution for

45 t^{4} + 32 t^{3} + 250 t - 200 = 0

using Newton-Raphson:

t \approx 0.70892 \dots

Apply long division:

\frac{45 t ^{4} + 32 t ^{3} + 250 t - 200}{t - 0.70892 \dots} = 45 t^{3} + 63.90179 \dots t^{2} + 45.30182 \dots t + 282.11576 \dots

45 t^{3} + 63.90179 \dots t^{2} + 45.30182 \dots t + 282.11576 \dots \approx 0

Find one solution for

45 t^{3} + 63.90179 \dots t^{2} + 45.30182 \dots t + 282.11576 \dots = 0

using Newton-Raphson:

t \approx - 2.22962 \dots

Apply long division:

\frac{45 t ^{3} + 63.90179 \dots t ^{2} + 45.30182 \dots t + 282.11576 \dots}{t + 2.22962 \dots} = 45 t^{2} - 36.43145 \dots t + 126.53042 \dots

45 t^{2} - 36.43145 \dots t + 126.53042 \dots \approx 0

Find one solution for

45 t^{2} - 36.43145 \dots t + 126.53042 \dots = 0

using Newton-Raphson:

No Solution for

t \in R

The solutions are

t \approx 0.70892 \dots, t \approx - 2.22962 \dots

4 q^{5} - 25 q^{3} = 0

x^{4} = e^{6}

2 x^{4} - 7 x^{3} + 21 x^{2} + 17 x - 13 = 0

x^{3} - 28 x - 48 = 0

x, (x - 1) (x - 1) (x - 1) = y

What are the solutions to the equation 4.5t^4+3.2t^3+25t=20 ?
The solutions to the equation 4.5t^4+3.2t^3+25t=20 are t\approx 0.70892…,t\approx-2.22962…
Find the zeros of 4.5t^4+3.2t^3+25t=20
The zeros of 4.5t^4+3.2t^3+25t=20 are t\approx 0.70892…,t\approx-2.22962…