Solve 3x^2 13x-10

Question

Simplify the expression

39 x^{3} - 10

Evaluate

3 x^{2} \times 13 x - 10

Solution

More Steps

Evaluate

3 x^{2} \times 13 x

Multiply the terms

39 x^{2} \times x

Multiply the terms with the same base by adding their exponents

39 x^{2 + 1}

Add the numbers

39 x^{3}

39 x^{3} - 10

Show Solution

x = \frac{3 15210}{39}

Alternative Form

x \approx 0.635299

Evaluate

3 x^{2} \times 13 x - 10

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

3 x^{2} \times 13 x - 10 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 13 x

Multiply the terms

39 x^{2} \times x

Multiply the terms with the same base by adding their exponents

39 x^{2 + 1}

Add the numbers

39 x^{3}

39 x^{3} - 10 = 0

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

39 x^{3} = 0 + 10

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

39 x^{3} = 10

Divide both sides

\frac{39 x ^{3}}{39} = \frac{10}{39}

Divide the numbers

x^{3} = \frac{10}{39}

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

3 x^{3} = 3 \frac{10}{39}

Calculate

x = 3 \frac{10}{39}

Solution

More Steps

Evaluate

3 \frac{10}{39}

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

\frac{3 10}{3 39}

Multiply by the Conjugate

\frac{3 10 \times 3 3 9 ^{2}}{3 39 \times 3 3 9 ^{2}}

Simplify

\frac{3 10 \times 3 1521}{3 39 \times 3 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 31521

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

3 10 \times 1521

Calculate the product

315210

\frac{3 15210}{3 39 \times 3 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

339 \times 3 3 9^{2}

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

3 39 \times 3 9^{2}

Calculate the product

3 3 9^{3}

Reduce the index of the radical and exponent with 3

39

\frac{3 15210}{39}

x = \frac{3 15210}{39}

Alternative Form

x \approx 0.635299

Show Solution