Solve 105x^3-(27)

Question

Factor the expression

3 (35 x^{3} - 9)

Evaluate

105 x^{3} - 27

Solution

3 (35 x^{3} - 9)

Show Solution

x = \frac{3 11025}{35}

Alternative Form

x \approx 0.635904

Evaluate

105 x^{3} - 27

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

105 x^{3} - 27 = 0

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

105 x^{3} = 0 + 27

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

105 x^{3} = 27

Divide both sides

\frac{105 x ^{3}}{105} = \frac{27}{105}

Divide the numbers

x^{3} = \frac{27}{105}

Cancel out the common factor 3

x^{3} = \frac{9}{35}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{9}{35}

Calculate

x = 3 \frac{9}{35}

Solution

More Steps

Evaluate

3 \frac{9}{35}

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

\frac{3 9}{3 35}

Multiply by the Conjugate

\frac{3 9 \times 3 3 5 ^{2}}{3 35 \times 3 3 5 ^{2}}

Simplify

\frac{3 9 \times 3 1225}{3 35 \times 3 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

39 \times 31225

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

3 9 \times 1225

Calculate the product

311025

\frac{3 11025}{3 35 \times 3 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

335 \times 3 3 5^{2}

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

3 35 \times 3 5^{2}

Calculate the product

3 3 5^{3}

Reduce the index of the radical and exponent with 3

35

\frac{3 11025}{35}

x = \frac{3 11025}{35}

Alternative Form

x \approx 0.635904

Show Solution