What are the solutions to the equation 10x^9-9x^{10}=0.75 ?

The solutions to the equation 10x^9-9x^{10}=0.75 are x\approx 1.06304…,x\approx 0.90359…

Find the zeros of 10x^9-9x^{10}=0.75

The zeros of 10x^9-9x^{10}=0.75 are x\approx 1.06304…,x\approx 0.90359…

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10 x^{9} - 9 x^{10} = 0.75

x \approx 1.06304 \dots, x \approx 0.90359 \dots

Solution steps

10 x^{9} - 9 x^{10} = 0.75

Multiply both sides by

100

1000 x^{9} - 900 x^{10} = 75

Move

75

to the left side

1000 x^{9} - 900 x^{10} - 75 = 0

Write in the standard form

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

- 900 x^{10} + 1000 x^{9} - 75 = 0

Find one solution for

- 900 x^{10} + 1000 x^{9} - 75 = 0

using Newton-Raphson:

x \approx 1.06304 \dots

Apply long division:

\frac{- 900 x ^{10} + 1000 x ^{9} - 75}{x - 1.06304 \dots} = - 900 x^{9} + 43.26200 \dots x^{8} + 45.98933 \dots x^{7} + 48.88860 \dots x^{6} + 51.97065 \dots x^{5} + 55.24700 \dots x^{4} + 58.72989 \dots x^{3} + 62.43235 \dots x^{2} + 66.36823 \dots x + 70.55223 \dots

- 900 x^{9} + 43.26200 \dots x^{8} + 45.98933 \dots x^{7} + 48.88860 \dots x^{6} + 51.97065 \dots x^{5} + 55.24700 \dots x^{4} + 58.72989 \dots x^{3} + 62.43235 \dots x^{2} + 66.36823 \dots x + 70.55223 \dots \approx 0

Find one solution for

- 900 x^{9} + 43.26200 \dots x^{8} + 45.98933 \dots x^{7} + 48.88860 \dots x^{6} + 51.97065 \dots x^{5} + 55.24700 \dots x^{4} + 58.72989 \dots x^{3} + 62.43235 \dots x^{2} + 66.36823 \dots x + 70.55223 \dots = 0

using Newton-Raphson:

x \approx 0.90359 \dots

Apply long division:

\frac{- 900 x ^{9} + 43.26200 \dots x ^{8} + 45.98933 \dots x ^{7} + 48.88860 \dots x ^{6} + 51.97065 \dots x ^{5} + 55.24700 \dots x ^{4} + 58.72989 \dots x ^{3} + 62.43235 \dots x ^{2} + 66.36823 \dots x + 70.55223 \dots}{x - 0.90359 \dots} = - 900 x^{8} - 769.97452 \dots x^{7} - 649.75667 \dots x^{6} - 538.22901 \dots x^{5} - 434.37101 \dots x^{4} - 337.24897 \dots x^{3} - 246.00697 \dots x^{2} - 159.85860 \dots x - 78.07938 \dots

- 900 x^{8} - 769.97452 \dots x^{7} - 649.75667 \dots x^{6} - 538.22901 \dots x^{5} - 434.37101 \dots x^{4} - 337.24897 \dots x^{3} - 246.00697 \dots x^{2} - 159.85860 \dots x - 78.07938 \dots \approx 0

Find one solution for

- 900 x^{8} - 769.97452 \dots x^{7} - 649.75667 \dots x^{6} - 538.22901 \dots x^{5} - 434.37101 \dots x^{4} - 337.24897 \dots x^{3} - 246.00697 \dots x^{2} - 159.85860 \dots x - 78.07938 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 1.06304 \dots, x \approx 0.90359 \dots

(2 z - i)^{3} = 33

(2 x - 1) (x^{2} + 2 x + 1) = 2 x^{2} + 2 x

x^{3} + 1

x^{7} - x^{4} - x^{3} + 1 = 0

4 x^{3} + 24 x^{2} = 0

What are the solutions to the equation 10x^9-9x^{10}=0.75 ?
The solutions to the equation 10x^9-9x^{10}=0.75 are x\approx 1.06304…,x\approx 0.90359…
Find the zeros of 10x^9-9x^{10}=0.75
The zeros of 10x^9-9x^{10}=0.75 are x\approx 1.06304…,x\approx 0.90359…