Solve 3x^2 21x-30

Question

Simplify the expression

63 x^{3} - 30

Evaluate

3 x^{2} \times 21 x - 30

Solution

More Steps

Evaluate

3 x^{2} \times 21 x

Multiply the terms

63 x^{2} \times x

Multiply the terms with the same base by adding their exponents

63 x^{2 + 1}

Add the numbers

63 x^{3}

63 x^{3} - 30

Show Solution

Factor the expression

3 (21 x^{3} - 10)

Evaluate

3 x^{2} \times 21 x - 30

Multiply

More Steps

Evaluate

3 x^{2} \times 21 x

Multiply the terms

63 x^{2} \times x

Multiply the terms with the same base by adding their exponents

63 x^{2 + 1}

Add the numbers

63 x^{3}

63 x^{3} - 30

Solution

3 (21 x^{3} - 10)

Show Solution

Find the roots

x = \frac{3 4410}{21}

Alternative Form

x \approx 0.780897

Evaluate

3 x^{2} \times 21 x - 30

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

3 x^{2} \times 21 x - 30 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 21 x

Multiply the terms

63 x^{2} \times x

Multiply the terms with the same base by adding their exponents

63 x^{2 + 1}

Add the numbers

63 x^{3}

63 x^{3} - 30 = 0

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

63 x^{3} = 0 + 30

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

63 x^{3} = 30

Divide both sides

\frac{63 x ^{3}}{63} = \frac{30}{63}

Divide the numbers

x^{3} = \frac{30}{63}

Cancel out the common factor 3

x^{3} = \frac{10}{21}

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

3 x^{3} = 3 \frac{10}{21}

Calculate

x = 3 \frac{10}{21}

Solution

More Steps

Evaluate

3 \frac{10}{21}

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

\frac{3 10}{3 21}

Multiply by the Conjugate

\frac{3 10 \times 3 2 1 ^{2}}{3 21 \times 3 2 1 ^{2}}

Simplify

\frac{3 10 \times 3 441}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 3441

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

3 10 \times 441

Calculate the product

34410

\frac{3 4410}{3 21 \times 3 2 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

321 \times 3 2 1^{2}

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

3 21 \times 2 1^{2}

Calculate the product

3 2 1^{3}

Reduce the index of the radical and exponent with 3

21

\frac{3 4410}{21}

x = \frac{3 4410}{21}

Alternative Form

x \approx 0.780897

Show Solution