Solve 3x^(2) 21x-54

Question

Simplify the expression

63 x^{3} - 54

Evaluate

3 x^{2} \times 21 x - 54

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} - 54

Show Solution

Factor the expression

9 (7 x^{3} - 6)

Evaluate

3 x^{2} \times 21 x - 54

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} - 54

Solution

9 (7 x^{3} - 6)

Show Solution

Find the roots

x = \frac{3 294}{7}

Alternative Form

x \approx 0.949914

Evaluate

3 x^{2} \times 21 x - 54

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

3 x^{2} \times 21 x - 54 = 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} - 54 = 0

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

63 x^{3} = 0 + 54

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

63 x^{3} = 54

Divide both sides

\frac{63 x ^{3}}{63} = \frac{54}{63}

Divide the numbers

x^{3} = \frac{54}{63}

Cancel out the common factor 9

x^{3} = \frac{6}{7}

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

3 x^{3} = 3 \frac{6}{7}

Calculate

x = 3 \frac{6}{7}

Solution

More Steps

Evaluate

3 \frac{6}{7}

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

\frac{3 6}{3 7}

Multiply by the Conjugate

\frac{3 6 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 6 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 349

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

3 6 \times 49

Calculate the product

3294

\frac{3 294}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 294}{7}

x = \frac{3 294}{7}

Alternative Form

x \approx 0.949914

Show Solution