Solve -27x^4 + 8 - ScanMath

Question

Find the roots

x_{1} = - \frac{4 24}{3}, x_{2} = \frac{4 24}{3}

Alternative Form

x_{1} \approx - 0.737788, x_{2} \approx 0.737788

Evaluate

- 27 x^{4} + 8

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

- 27 x^{4} + 8 = 0

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

- 27 x^{4} = 0 - 8

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

- 27 x^{4} = - 8

Change the signs on both sides of the equation

27 x^{4} = 8

Divide both sides

\frac{27 x ^{4}}{27} = \frac{8}{27}

Divide the numbers

x^{4} = \frac{8}{27}

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

x = \pm 4 \frac{8}{27}

Simplify the expression

More Steps

Evaluate

4 \frac{8}{27}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 8}{4 27}

Multiply by the Conjugate

\frac{4 8 \times 4 2 7 ^{3}}{4 27 \times 4 2 7 ^{3}}

Simplify

\frac{4 8 \times 3 ^{2} 4 3}{4 27 \times 4 2 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

48 \times 3^{2} 43

Multiply the terms

424 \times 3^{2}

Use the commutative property to reorder the terms

3^{2} 424

\frac{3 ^{2} 4 24}{4 27 \times 4 2 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

427 \times 4 2 7^{3}

The product of roots with the same index is equal to the root of the product

4 27 \times 2 7^{3}

Calculate the product

4 2 7^{4}

Transform the expression

4 3^{12}

Reduce the index of the radical and exponent with 4

3^{3}

\frac{3 ^{2} 4 24}{3 ^{3}}

Reduce the fraction

More Steps

Evaluate

\frac{3 ^{2}}{3 ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{3 ^{3 - 2}}

Subtract the terms

\frac{1}{3 ^{1}}

Simplify

\frac{1}{3}

\frac{4 24}{3}

x = \pm \frac{4 24}{3}

Separate the equation into 2 possible cases

x = \frac{4 24}{3} x = - \frac{4 24}{3}

Solution

x_{1} = - \frac{4 24}{3}, x_{2} = \frac{4 24}{3}

Alternative Form

x_{1} \approx - 0.737788, x_{2} \approx 0.737788

Show Solution