Solve 3x^2 10x-13

Question

Simplify the expression

30 x^{3} - 13

Evaluate

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

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} - 13

Show Solution

x = \frac{3 11700}{30}

Alternative Form

x \approx 0.75673

Evaluate

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

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

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

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

30 x^{3} = 0 + 13

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

30 x^{3} = 13

Divide both sides

\frac{30 x ^{3}}{30} = \frac{13}{30}

Divide the numbers

x^{3} = \frac{13}{30}

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

3 x^{3} = 3 \frac{13}{30}

Calculate

x = 3 \frac{13}{30}

Solution

More Steps

Evaluate

3 \frac{13}{30}

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

\frac{3 13}{3 30}

Multiply by the Conjugate

\frac{3 13 \times 3 3 0 ^{2}}{3 30 \times 3 3 0 ^{2}}

Simplify

\frac{3 13 \times 3 900}{3 30 \times 3 3 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3900

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

3 13 \times 900

Calculate the product

311700

\frac{3 11700}{3 30 \times 3 3 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

330 \times 3 3 0^{2}

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

3 30 \times 3 0^{2}

Calculate the product

3 3 0^{3}

Reduce the index of the radical and exponent with 3

30

\frac{3 11700}{30}

x = \frac{3 11700}{30}

Alternative Form

x \approx 0.75673

Show Solution