Solve 28x^(3)-125

Question

Find the roots

x = \frac{5 3 98}{14}

Alternative Form

x \approx 1.646584

Evaluate

28 x^{3} - 125

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

28 x^{3} - 125 = 0

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

28 x^{3} = 0 + 125

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

28 x^{3} = 125

Divide both sides

\frac{28 x ^{3}}{28} = \frac{125}{28}

Divide the numbers

x^{3} = \frac{125}{28}

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

3 x^{3} = 3 \frac{125}{28}

Calculate

x = 3 \frac{125}{28}

Solution

More Steps

Evaluate

3 \frac{125}{28}

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

\frac{3 125}{3 28}

Simplify the radical expression

More Steps

Evaluate

3125

Write the number in exponential form with the base of 5

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{5}{3 28}

Multiply by the Conjugate

\frac{5 3 2 8 ^{2}}{3 28 \times 3 2 8 ^{2}}

Simplify

\frac{5 \times 2 3 98}{3 28 \times 3 2 8 ^{2}}

Multiply the numbers

\frac{10 3 98}{3 28 \times 3 2 8 ^{2}}

Multiply the numbers

More Steps

Evaluate

328 \times 3 2 8^{2}

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

3 28 \times 2 8^{2}

Calculate the product

3 2 8^{3}

Reduce the index of the radical and exponent with 3

28

\frac{10 3 98}{28}

Cancel out the common factor 2

\frac{5 3 98}{14}

x = \frac{5 3 98}{14}

Alternative Form

x \approx 1.646584

Show Solution