Solve 3x^2 18x-48

Question

Simplify the expression

54 x^{3} - 48

Evaluate

3 x^{2} \times 18 x - 48

Solution

More Steps

Evaluate

3 x^{2} \times 18 x

Multiply the terms

54 x^{2} \times x

Multiply the terms with the same base by adding their exponents

54 x^{2 + 1}

Add the numbers

54 x^{3}

54 x^{3} - 48

Show Solution

Factor the expression

6 (9 x^{3} - 8)

Evaluate

3 x^{2} \times 18 x - 48

Multiply

More Steps

Evaluate

3 x^{2} \times 18 x

Multiply the terms

54 x^{2} \times x

Multiply the terms with the same base by adding their exponents

54 x^{2 + 1}

Add the numbers

54 x^{3}

54 x^{3} - 48

Solution

6 (9 x^{3} - 8)

Show Solution

Find the roots

x = \frac{2 3 3}{3}

Alternative Form

x \approx 0.9615

Evaluate

3 x^{2} \times 18 x - 48

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

3 x^{2} \times 18 x - 48 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times 18 x

Multiply the terms

54 x^{2} \times x

Multiply the terms with the same base by adding their exponents

54 x^{2 + 1}

Add the numbers

54 x^{3}

54 x^{3} - 48 = 0

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

54 x^{3} = 0 + 48

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

54 x^{3} = 48

Divide both sides

\frac{54 x ^{3}}{54} = \frac{48}{54}

Divide the numbers

x^{3} = \frac{48}{54}

Cancel out the common factor 6

x^{3} = \frac{8}{9}

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

3 x^{3} = 3 \frac{8}{9}

Calculate

x = 3 \frac{8}{9}

Solution

More Steps

Evaluate

3 \frac{8}{9}

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

\frac{3 8}{3 9}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{2}{3 9}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

\frac{6 3 3}{3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

39 \times 3 9^{2}

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

3 9 \times 9^{2}

Calculate the product

3 9^{3}

Transform the expression

3 3^{6}

Reduce the index of the radical and exponent with 3

3^{2}

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

Rewrite the expression

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

Reduce the fraction

More Steps

Evaluate

\frac{3}{3 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{3 ^{2 - 1}}

Subtract the terms

\frac{1}{3 ^{1}}

Simplify

\frac{1}{3}

\frac{2 3 3}{3}

x = \frac{2 3 3}{3}

Alternative Form

x \approx 0.9615

Show Solution