Solve 3x^(2) 10x-125

Question

Simplify the expression

30 x^{3} - 125

Evaluate

3 x^{2} \times 10 x - 125

Solution

More Steps

Evaluate

3 x^{2} \times 10 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

30 x^{3} - 125

Show Solution

Factor the expression

5 (6 x^{3} - 25)

Evaluate

3 x^{2} \times 10 x - 125

Multiply

More Steps

Evaluate

3 x^{2} \times 10 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

30 x^{3} - 125

Solution

5 (6 x^{3} - 25)

Show Solution

Find the roots

x = \frac{3 900}{6}

Alternative Form

x \approx 1.609149

Evaluate

3 x^{2} \times 10 x - 125

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

3 x^{2} \times 10 x - 125 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 10 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

30 x^{3} - 125 = 0

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

30 x^{3} = 0 + 125

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

30 x^{3} = 125

Divide both sides

\frac{30 x ^{3}}{30} = \frac{125}{30}

Divide the numbers

x^{3} = \frac{125}{30}

Cancel out the common factor 5

x^{3} = \frac{25}{6}

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

3 x^{3} = 3 \frac{25}{6}

Calculate

x = 3 \frac{25}{6}

Solution

More Steps

Evaluate

3 \frac{25}{6}

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

\frac{3 25}{3 6}

Multiply by the Conjugate

\frac{3 25 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{3 25 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

325 \times 336

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

3 25 \times 36

Calculate the product

3900

\frac{3 900}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 3 6^{2}

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

3 6 \times 6^{2}

Calculate the product

3 6^{3}

Reduce the index of the radical and exponent with 3

6

\frac{3 900}{6}

x = \frac{3 900}{6}

Alternative Form

x \approx 1.609149

Show Solution