What are the solutions to the equation 5x+67=3x+175(x^9) ?

The solutions to the equation 5x+67=3x+175(x^9) are x\approx 0.90147…

Find the zeros of 5x+67=3x+175(x^9)

The zeros of 5x+67=3x+175(x^9) are x\approx 0.90147…

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5 x + 67 = 3 x + 175 (x^{9})

x \approx 0.90147 \dots

Solution steps

5 x + 67 = 3 x + 175 (x^{9})

Refine

5 x + 67 = 3 x + 175 x^{9}

Switch sides

3 x + 175 x^{9} = 5 x + 67

Move

67

to the left side

3 x + 175 x^{9} - 67 = 5 x

Move

5 x

to the left side

175 x^{9} - 2 x - 67 = 0

Find one solution for

175 x^{9} - 2 x - 67 = 0

using Newton-Raphson:

x \approx 0.90147 \dots

Apply long division:

\frac{175 x ^{9} - 2 x - 67}{x - 0.90147 \dots} = 175 x^{8} + 157.75755 \dots x^{7} + 142.21397 \dots x^{6} + 128.20187 \dots x^{5} + 115.57036 \dots x^{4} + 104.18341 \dots x^{3} + 93.91840 \dots x^{2} + 84.66478 \dots x + 74.32290 \dots

175 x^{8} + 157.75755 \dots x^{7} + 142.21397 \dots x^{6} + 128.20187 \dots x^{5} + 115.57036 \dots x^{4} + 104.18341 \dots x^{3} + 93.91840 \dots x^{2} + 84.66478 \dots x + 74.32290 \dots \approx 0

Find one solution for

175 x^{8} + 157.75755 \dots x^{7} + 142.21397 \dots x^{6} + 128.20187 \dots x^{5} + 115.57036 \dots x^{4} + 104.18341 \dots x^{3} + 93.91840 \dots x^{2} + 84.66478 \dots x + 74.32290 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx 0.90147 \dots

x^{2} - 6 x + 6 \geq 0

\frac{10 - 5 i}{6 + 2 i}

8 - ∣ 3 x + 2 ∣ = 3

\frac{2 x - 1}{3} - \frac{3 x}{4} = \frac{5}{6}

\frac{7}{4} - \frac{7}{12}

What are the solutions to the equation 5x+67=3x+175(x^9) ?
The solutions to the equation 5x+67=3x+175(x^9) are x\approx 0.90147…
Find the zeros of 5x+67=3x+175(x^9)
The zeros of 5x+67=3x+175(x^9) are x\approx 0.90147…