Solve x^4-5x^3 27x-27

Question

Simplify the expression

- 134 x^{4} - 27

Show Solution

x_{1} = - \frac{4 54 \times 6 7 ^{3}}{134} - \frac{4 54 \times 6 7 ^{3}}{134} i, x_{2} = \frac{4 54 \times 6 7 ^{3}}{134} + \frac{4 54 \times 6 7 ^{3}}{134} i

Alternative Form

x_{1} \approx - 0.473751 - 0.473751 i, x_{2} \approx 0.473751 + 0.473751 i

Evaluate

x^{4} - 5 x^{3} \times 27 x - 27

To find the roots of the expression,set the expression equal to 0

x^{4} - 5 x^{3} \times 27 x - 27 = 0

Multiply

More Steps

x^{4} - 135 x^{4} - 27 = 0

Subtract the terms

More Steps

- 134 x^{4} - 27 = 0

Move the constant to the right-hand side and change its sign

- 134 x^{4} = 0 + 27

Removing 0 doesn't change the value,so remove it from the expression

- 134 x^{4} = 27

Change the signs on both sides of the equation

134 x^{4} = - 27

Divide both sides

\frac{134 x ^{4}}{134} = \frac{- 27}{134}

Divide the numbers

x^{4} = \frac{- 27}{134}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{4} = - \frac{27}{134}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 - \frac{27}{134}

Simplify the expression

More Steps

x = \pm (\frac{4 54 \times 6 7 ^{3}}{134} + \frac{4 54 \times 6 7 ^{3}}{134} i)

Separate the equation into 2 possible cases

x = \frac{4 54 \times 6 7 ^{3}}{134} + \frac{4 54 \times 6 7 ^{3}}{134} i x = - \frac{4 54 \times 6 7 ^{3}}{134} - \frac{4 54 \times 6 7 ^{3}}{134} i

Solution

x_{1} = - \frac{4 54 \times 6 7 ^{3}}{134} - \frac{4 54 \times 6 7 ^{3}}{134} i, x_{2} = \frac{4 54 \times 6 7 ^{3}}{134} + \frac{4 54 \times 6 7 ^{3}}{134} i

Alternative Form

x_{1} \approx - 0.473751 - 0.473751 i, x_{2} \approx 0.473751 + 0.473751 i

Show Solution