What are the solutions to the equation 0.5(5-7x)=8-(4x^6) ?

The solutions to the equation 0.5(5-7x)=8-(4x^6) are x\approx-0.91234…,x\approx 1.15600…

Find the zeros of 0.5(5-7x)=8-(4x^6)

The zeros of 0.5(5-7x)=8-(4x^6) are x\approx-0.91234…,x\approx 1.15600…

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0.5 (5 - 7 x) = 8 - (4 x^{6})

x \approx - 0.91234 \dots, x \approx 1.15600 \dots

Solution steps

0.5 (5 - 7 x) = 8 - (4 x^{6})

Multiply both sides by

10

5 (5 - 7 x) = 80 - 40 x^{6}

Expand

5 (5 - 7 x) : 25 - 35 x

25 - 35 x = 80 - 40 x^{6}

Switch sides

80 - 40 x^{6} = 25 - 35 x

Move

35 x

to the left side

80 - 40 x^{6} + 35 x = 25

Move

25

to the left side

- 40 x^{6} + 35 x + 55 = 0

Find one solution for

- 40 x^{6} + 35 x + 55 = 0

using Newton-Raphson:

x \approx - 0.91234 \dots

Apply long division:

\frac{- 40 x ^{6} + 35 x + 55}{x + 0.91234 \dots} = - 40 x^{5} + 36.49373 \dots x^{4} - 33.29481 \dots x^{3} + 30.37629 \dots x^{2} - 27.71361 \dots x + 60.28432 \dots

- 40 x^{5} + 36.49373 \dots x^{4} - 33.29481 \dots x^{3} + 30.37629 \dots x^{2} - 27.71361 \dots x + 60.28432 \dots \approx 0

Find one solution for

- 40 x^{5} + 36.49373 \dots x^{4} - 33.29481 \dots x^{3} + 30.37629 \dots x^{2} - 27.71361 \dots x + 60.28432 \dots = 0

using Newton-Raphson:

x \approx 1.15600 \dots

Apply long division:

\frac{- 40 x ^{5} + 36.49373 \dots x ^{4} - 33.29481 \dots x ^{3} + 30.37629 \dots x ^{2} - 27.71361 \dots x + 60.28432 \dots}{x - 1.15600 \dots} = - 40 x^{4} - 9.74654 \dots x^{3} - 44.56188 \dots x^{2} - 21.13754 \dots x - 52.14876 \dots

- 40 x^{4} - 9.74654 \dots x^{3} - 44.56188 \dots x^{2} - 21.13754 \dots x - 52.14876 \dots \approx 0

Find one solution for

- 40 x^{4} - 9.74654 \dots x^{3} - 44.56188 \dots x^{2} - 21.13754 \dots x - 52.14876 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx - 0.91234 \dots, x \approx 1.15600 \dots

x, x^{4} + y^{4} = 2

125000 (x)^{6} = 165000

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

x^{3} - 24 x + 32 = 0

x (x^{2} + 3) = 8

What are the solutions to the equation 0.5(5-7x)=8-(4x^6) ?
The solutions to the equation 0.5(5-7x)=8-(4x^6) are x\approx-0.91234…,x\approx 1.15600…
Find the zeros of 0.5(5-7x)=8-(4x^6)
The zeros of 0.5(5-7x)=8-(4x^6) are x\approx-0.91234…,x\approx 1.15600…