What are the solutions to the equation 5x^6-(3-2x)8=(4x-3)12 ?

The solutions to the equation 5x^6-(3-2x)8=(4x-3)12 are x\approx 0.37543…,x\approx 1.35890…

Find the zeros of 5x^6-(3-2x)8=(4x-3)12

The zeros of 5x^6-(3-2x)8=(4x-3)12 are x\approx 0.37543…,x\approx 1.35890…

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5 x^{6} - (3 - 2 x) 8 = (4 x - 3) 12

x \approx 0.37543 \dots, x \approx 1.35890 \dots

Solution steps

5 x^{6} - (3 - 2 x) \cdot 8 = (4 x - 3) \cdot 12

Expand

5 x^{6} - (3 - 2 x) \cdot 8 : 5 x^{6} - 24 + 16 x

Expand

(4 x - 3) \cdot 12 : 48 x - 36

5 x^{6} - 24 + 16 x = 48 x - 36

Move

36

to the left side

5 x^{6} + 16 x + 12 = 48 x

Move

48 x

to the left side

5 x^{6} - 32 x + 12 = 0

Find one solution for

5 x^{6} - 32 x + 12 = 0

using Newton-Raphson:

x \approx 0.37543 \dots

Apply long division:

\frac{5 x ^{6} - 32 x + 12}{x - 0.37543 \dots} = 5 x^{5} + 1.87718 \dots x^{4} + 0.70476 \dots x^{3} + 0.26459 \dots x^{2} + 0.09933 \dots x - 31.96270 \dots

5 x^{5} + 1.87718 \dots x^{4} + 0.70476 \dots x^{3} + 0.26459 \dots x^{2} + 0.09933 \dots x - 31.96270 \dots \approx 0

Find one solution for

5 x^{5} + 1.87718 \dots x^{4} + 0.70476 \dots x^{3} + 0.26459 \dots x^{2} + 0.09933 \dots x - 31.96270 \dots = 0

using Newton-Raphson:

x \approx 1.35890 \dots

Apply long division:

\frac{5 x ^{5} + 1.87718 \dots x ^{4} + 0.70476 \dots x ^{3} + 0.26459 \dots x ^{2} + 0.09933 \dots x - 31.96270 \dots}{x - 1.35890 \dots} = 5 x^{4} + 8.67170 \dots x^{3} + 12.48878 \dots x^{2} + 17.23565 \dots x + 23.52094 \dots

5 x^{4} + 8.67170 \dots x^{3} + 12.48878 \dots x^{2} + 17.23565 \dots x + 23.52094 \dots \approx 0

Find one solution for

5 x^{4} + 8.67170 \dots x^{3} + 12.48878 \dots x^{2} + 17.23565 \dots x + 23.52094 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.37543 \dots, x \approx 1.35890 \dots

x^{3} - 6 x^{2} - 15 x + 90 = 0

x, 4 x^{3} + 4 y = 0

3 x^{3} + 9 x^{2} + 8 x = 0

2 x^{3} - 7 x^{2} + x + 10 = 0

(x - 3)^{10} = 0

What are the solutions to the equation 5x^6-(3-2x)8=(4x-3)12 ?
The solutions to the equation 5x^6-(3-2x)8=(4x-3)12 are x\approx 0.37543…,x\approx 1.35890…
Find the zeros of 5x^6-(3-2x)8=(4x-3)12
The zeros of 5x^6-(3-2x)8=(4x-3)12 are x\approx 0.37543…,x\approx 1.35890…