What are the solutions to the equation 2^2x-5=3x^2-12x^{31} ?

The solutions to the equation 2^2x-5=3x^2-12x^{31} are x\approx 0.96465…

Find the zeros of 2^2x-5=3x^2-12x^{31}

The zeros of 2^2x-5=3x^2-12x^{31} are x\approx 0.96465…

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2^{2} x - 5 = 3 x^{2} - 12 x^{31}

x \approx 0.96465 \dots

Solution steps

2^{2} x - 5 = 3 x^{2} - 12 x^{31}

Expand

2^{2} x - 5 : 4 x - 5

4 x - 5 = 3 x^{2} - 12 x^{31}

Switch sides

3 x^{2} - 12 x^{31} = 4 x - 5

Move

5

to the left side

3 x^{2} - 12 x^{31} + 5 = 4 x

Move

4 x

to the left side

3 x^{2} - 12 x^{31} + 5 - 4 x = 0

Write in the standard form

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

- 12 x^{31} + 3 x^{2} - 4 x + 5 = 0

Find one solution for

- 12 x^{31} + 3 x^{2} - 4 x + 5 = 0

using Newton-Raphson:

x \approx 0.96465 \dots

Apply long division:

\frac{- 12 x ^{31} + 3 x ^{2} - 4 x + 5}{x - 0.96465 \dots} = - 12 x^{30} - 11.57587 \dots x^{29} - 11.16673 \dots x^{28} - 10.77206 \dots x^{27} - 10.39133 \dots x^{26} - 10.02406 \dots x^{25} - 9.66978 \dots x^{24} - 9.32801 \dots x^{23} - 8.99832 \dots x^{22} - 8.68029 \dots x^{21} - 8.37349 \dots x^{20} - 8.07754 \dots x^{19} - 7.79205 \dots x^{18} - 7.51665 \dots x^{17} - 7.25098 \dots x^{16} - 6.99470 \dots x^{15} - 6.74748 \dots x^{14} - 6.50900 \dots x^{13} - 6.27895 \dots x^{12} - 6.05703 \dots x^{11} - 5.84295 \dots x^{10} - 5.63644 \dots x^{9} - 5.43722 \dots x^{8} - 5.24505 \dots x^{7} - 5.05967 \dots x^{6} - 4.88084 \dots x^{5} - 4.70833 \dots x^{4} - 4.54192 \dots x^{3} - 4.38139 \dots x^{2} - 1.22654 \dots x - 5.18319 \dots

- 12 x^{30} - 11.57587 \dots x^{29} - 11.16673 \dots x^{28} - 10.77206 \dots x^{27} - 10.39133 \dots x^{26} - 10.02406 \dots x^{25} - 9.66978 \dots x^{24} - 9.32801 \dots x^{23} - 8.99832 \dots x^{22} - 8.68029 \dots x^{21} - 8.37349 \dots x^{20} - 8.07754 \dots x^{19} - 7.79205 \dots x^{18} - 7.51665 \dots x^{17} - 7.25098 \dots x^{16} - 6.99470 \dots x^{15} - 6.74748 \dots x^{14} - 6.50900 \dots x^{13} - 6.27895 \dots x^{12} - 6.05703 \dots x^{11} - 5.84295 \dots x^{10} - 5.63644 \dots x^{9} - 5.43722 \dots x^{8} - 5.24505 \dots x^{7} - 5.05967 \dots x^{6} - 4.88084 \dots x^{5} - 4.70833 \dots x^{4} - 4.54192 \dots x^{3} - 4.38139 \dots x^{2} - 1.22654 \dots x - 5.18319 \dots \approx 0

Find one solution for

- 12 x^{30} - 11.57587 \dots x^{29} - 11.16673 \dots x^{28} - 10.77206 \dots x^{27} - 10.39133 \dots x^{26} - 10.02406 \dots x^{25} - 9.66978 \dots x^{24} - 9.32801 \dots x^{23} - 8.99832 \dots x^{22} - 8.68029 \dots x^{21} - 8.37349 \dots x^{20} - 8.07754 \dots x^{19} - 7.79205 \dots x^{18} - 7.51665 \dots x^{17} - 7.25098 \dots x^{16} - 6.99470 \dots x^{15} - 6.74748 \dots x^{14} - 6.50900 \dots x^{13} - 6.27895 \dots x^{12} - 6.05703 \dots x^{11} - 5.84295 \dots x^{10} - 5.63644 \dots x^{9} - 5.43722 \dots x^{8} - 5.24505 \dots x^{7} - 5.05967 \dots x^{6} - 4.88084 \dots x^{5} - 4.70833 \dots x^{4} - 4.54192 \dots x^{3} - 4.38139 \dots x^{2} - 1.22654 \dots x - 5.18319 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.96465 \dots

5 x^{3} + 15 x^{2} - 20 x = 0

x, x^{4} - 9 x^{2} - y = 0

x^{6} + 6 x^{3} - 7 = 0

12 (x^{3} - 4 x^{2} + x + 6) = 0

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

What are the solutions to the equation 2^2x-5=3x^2-12x^{31} ?
The solutions to the equation 2^2x-5=3x^2-12x^{31} are x\approx 0.96465…
Find the zeros of 2^2x-5=3x^2-12x^{31}
The zeros of 2^2x-5=3x^2-12x^{31} are x\approx 0.96465…