Solve 5x^348x - 8

Question

Simplify the expression

240 x^{4} - 8

Evaluate

5 x^{3} \times 48 x - 8

Solution

More Steps

Evaluate

5 x^{3} \times 48 x

Multiply the terms

240 x^{3} \times x

Multiply the terms with the same base by adding their exponents

240 x^{3 + 1}

Add the numbers

240 x^{4}

240 x^{4} - 8

Show Solution

Factor the expression

8 (30 x^{4} - 1)

Evaluate

5 x^{3} \times 48 x - 8

Multiply

More Steps

Evaluate

5 x^{3} \times 48 x

Multiply the terms

240 x^{3} \times x

Multiply the terms with the same base by adding their exponents

240 x^{3 + 1}

Add the numbers

240 x^{4}

240 x^{4} - 8

Solution

8 (30 x^{4} - 1)

Show Solution

Find the roots

x_{1} = - \frac{4 27000}{30}, x_{2} = \frac{4 27000}{30}

Alternative Form

x_{1} \approx - 0.427287, x_{2} \approx 0.427287

Evaluate

5 x^{3} \times 48 x - 8

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

5 x^{3} \times 48 x - 8 = 0

Multiply

More Steps

Multiply the terms

5 x^{3} \times 48 x

Multiply the terms

240 x^{3} \times x

Multiply the terms with the same base by adding their exponents

240 x^{3 + 1}

Add the numbers

240 x^{4}

240 x^{4} - 8 = 0

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

240 x^{4} = 0 + 8

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

240 x^{4} = 8

Divide both sides

\frac{240 x ^{4}}{240} = \frac{8}{240}

Divide the numbers

x^{4} = \frac{8}{240}

Cancel out the common factor 8

x^{4} = \frac{1}{30}

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

x = \pm 4 \frac{1}{30}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{30}

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

\frac{4 1}{4 30}

Simplify the radical expression

\frac{1}{4 30}

Multiply by the Conjugate

\frac{4 3 0 ^{3}}{4 30 \times 4 3 0 ^{3}}

Simplify

\frac{4 27000}{4 30 \times 4 3 0 ^{3}}

Multiply the numbers

More Steps

Evaluate

430 \times 4 3 0^{3}

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

4 30 \times 3 0^{3}

Calculate the product

4 3 0^{4}

Reduce the index of the radical and exponent with 4

30

\frac{4 27000}{30}

x = \pm \frac{4 27000}{30}

Separate the equation into 2 possible cases

x = \frac{4 27000}{30} x = - \frac{4 27000}{30}

Solution

x_{1} = - \frac{4 27000}{30}, x_{2} = \frac{4 27000}{30}

Alternative Form

x_{1} \approx - 0.427287, x_{2} \approx 0.427287

Show Solution