Solve 9x^311x^23x - 33

Question

Simplify the expression

297 x^{6} - 33

Evaluate

9 x^{3} \times 11 x^{2} \times 3 x - 33

Solution

More Steps

Evaluate

9 x^{3} \times 11 x^{2} \times 3 x

Multiply the terms

More Steps

Evaluate

9 \times 11 \times 3

Multiply the terms

99 \times 3

Multiply the numbers

297

297 x^{3} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

297 x^{3 + 2 + 1}

Add the numbers

297 x^{6}

297 x^{6} - 33

Show Solution

Factor the expression

33 (3 x^{3} - 1) (3 x^{3} + 1)

Evaluate

9 x^{3} \times 11 x^{2} \times 3 x - 33

Evaluate

More Steps

Evaluate

9 x^{3} \times 11 x^{2} \times 3 x

Multiply the terms

More Steps

Evaluate

9 \times 11 \times 3

Multiply the terms

99 \times 3

Multiply the numbers

297

297 x^{3} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

297 x^{3 + 2 + 1}

Add the numbers

297 x^{6}

297 x^{6} - 33

Factor out 33 from the expression

33 (9 x^{6} - 1)

Solution

More Steps

Evaluate

9 x^{6} - 1

Rewrite the expression in exponential form

(3 x^{3})^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(3 x^{3} - 1) (3 x^{3} + 1)

33 (3 x^{3} - 1) (3 x^{3} + 1)

Show Solution

Find the roots

x_{1} = - \frac{3 9}{3}, x_{2} = \frac{3 9}{3}

Alternative Form

x_{1} \approx - 0.693361, x_{2} \approx 0.693361

Evaluate

9 x^{3} \times 11 x^{2} \times 3 x - 33

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

9 x^{3} \times 11 x^{2} \times 3 x - 33 = 0

Multiply

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Multiply the terms

9 x^{3} \times 11 x^{2} \times 3 x

Multiply the terms

More Steps

Evaluate

9 \times 11 \times 3

Multiply the terms

99 \times 3

Multiply the numbers

297

297 x^{3} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

297 x^{3 + 2 + 1}

Add the numbers

297 x^{6}

297 x^{6} - 33 = 0

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

297 x^{6} = 0 + 33

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

297 x^{6} = 33

Divide both sides

\frac{297 x ^{6}}{297} = \frac{33}{297}

Divide the numbers

x^{6} = \frac{33}{297}

Cancel out the common factor 33

x^{6} = \frac{1}{9}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 6 \frac{1}{9}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{9}

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

\frac{6 1}{6 9}

Simplify the radical expression

\frac{1}{6 9}

Simplify the radical expression

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Evaluate

69

Write the number in exponential form with the base of 3

6 3^{2}

Reduce the index of the radical and exponent with 2

33

\frac{1}{3 3}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 9}{3}

x = \pm \frac{3 9}{3}

Separate the equation into 2 possible cases

x = \frac{3 9}{3} x = - \frac{3 9}{3}

Solution

x_{1} = - \frac{3 9}{3}, x_{2} = \frac{3 9}{3}

Alternative Form

x_{1} \approx - 0.693361, x_{2} \approx 0.693361

Show Solution