What are the solutions to the equation 13e^9e+4=-5e+14+13e^9 ?

The solutions to the equation 13e^9e+4=-5e+14+13e^9 are e\approx 1.12097…,e\approx-0.94175…

Find the zeros of 13e^9e+4=-5e+14+13e^9

The zeros of 13e^9e+4=-5e+14+13e^9 are e\approx 1.12097…,e\approx-0.94175…

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13 e^{9} e + 4 = - 5 e + 14 + 13 e^{9}

e \approx 1.12097 \dots, e \approx - 0.94175 \dots

Solution steps

13 e^{9} e + 4 = - 5 e + 14 + 13 e^{9}

Expand

13 e^{9} e + 4 : 13 e^{10} + 4

13 e^{10} + 4 = - 5 e + 14 + 13 e^{9}

Move

13 e^{9}

to the left side

13 e^{10} + 4 - 13 e^{9} = - 5 e + 14

Move

14

to the left side

13 e^{10} - 13 e^{9} - 10 = - 5 e

Move

5 e

to the left side

13 e^{10} - 13 e^{9} - 10 + 5 e = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

13 e^{10} - 13 e^{9} + 5 e - 10 = 0

Find one solution for

13 e^{10} - 13 e^{9} + 5 e - 10 = 0

using Newton-Raphson:

e \approx 1.12097 \dots

Apply long division:

\frac{13 e ^{10} - 13 e ^{9} + 5 e - 10}{e - 1.12097 \dots} = 13 e^{9} + 1.57262 \dots e^{8} + 1.76286 \dots e^{7} + 1.97611 \dots e^{6} + 2.21517 \dots e^{5} + 2.48314 \dots e^{4} + 2.78353 \dots e^{3} + 3.12025 \dots e^{2} + 3.49771 \dots e + 8.92083 \dots

13 e^{9} + 1.57262 \dots e^{8} + 1.76286 \dots e^{7} + 1.97611 \dots e^{6} + 2.21517 \dots e^{5} + 2.48314 \dots e^{4} + 2.78353 \dots e^{3} + 3.12025 \dots e^{2} + 3.49771 \dots e + 8.92083 \dots \approx 0

Find one solution for

13 e^{9} + 1.57262 \dots e^{8} + 1.76286 \dots e^{7} + 1.97611 \dots e^{6} + 2.21517 \dots e^{5} + 2.48314 \dots e^{4} + 2.78353 \dots e^{3} + 3.12025 \dots e^{2} + 3.49771 \dots e + 8.92083 \dots = 0

using Newton-Raphson:

e \approx - 0.94175 \dots

Apply long division:

\frac{13 e ^{9} + 1.57262 \dots e ^{8} + 1.76286 \dots e ^{7} + 1.97611 \dots e ^{6} + 2.21517 \dots e ^{5} + 2.48314 \dots e ^{4} + 2.78353 \dots e ^{3} + 3.12025 \dots e ^{2} + 3.49771 \dots e + 8.92083 \dots}{e + 0.94175 \dots} = 13 e^{8} - 10.67018 \dots e^{7} + 11.81155 \dots e^{6} - 9.14746 \dots e^{5} + 10.82983 \dots e^{4} - 7.71590 \dots e^{3} + 10.05001 \dots e^{2} - 6.34439 \dots e + 9.47257 \dots

13 e^{8} - 10.67018 \dots e^{7} + 11.81155 \dots e^{6} - 9.14746 \dots e^{5} + 10.82983 \dots e^{4} - 7.71590 \dots e^{3} + 10.05001 \dots e^{2} - 6.34439 \dots e + 9.47257 \dots \approx 0

Find one solution for

13 e^{8} - 10.67018 \dots e^{7} + 11.81155 \dots e^{6} - 9.14746 \dots e^{5} + 10.82983 \dots e^{4} - 7.71590 \dots e^{3} + 10.05001 \dots e^{2} - 6.34439 \dots e + 9.47257 \dots = 0

using Newton-Raphson:

No Solution for

e \in R

The solutions are

e \approx 1.12097 \dots, e \approx - 0.94175 \dots

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

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

9 y^{4} + 65 y^{2} - 144 = 0

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

x^{4} + x^{3} - 6 x^{2} - 4 x + 8 = 0

What are the solutions to the equation 13e^9e+4=-5e+14+13e^9 ?
The solutions to the equation 13e^9e+4=-5e+14+13e^9 are e\approx 1.12097…,e\approx-0.94175…
Find the zeros of 13e^9e+4=-5e+14+13e^9
The zeros of 13e^9e+4=-5e+14+13e^9 are e\approx 1.12097…,e\approx-0.94175…