Trigonometry Examples

$7 x^{2} \cdot (9 x) + 2 = 0$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$7 \cdot 9 x^{2} x + 2 = 0$

Step 1.2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.2.1

Move $x$ .

$7 \cdot 9 (x \cdot x^{2}) + 2 = 0$

Step 1.2.2

Multiply $x$ by $x^{2}$ .

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Step 1.2.2.1

Raise $x$ to the power of $1$ .

$7 \cdot 9 (x^{1} x^{2}) + 2 = 0$

Step 1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7 \cdot 9 x^{1 + 2} + 2 = 0$

Step 1.2.3

Add $1$ and $2$ .

$7 \cdot 9 x^{3} + 2 = 0$

Step 1.3

Multiply $7$ by $9$ .

$63 x^{3} + 2 = 0$

Step 2

Subtract $2$ from both sides of the equation.

$63 x^{3} = - 2$

Step 3

Divide each term in $63 x^{3} = - 2$ by $63$ and simplify.

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Step 3.1

Divide each term in $63 x^{3} = - 2$ by $63$ .

$\frac{63 x^{3}}{63} = \frac{- 2}{63}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $63$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{63 x^{3}}{63} = \frac{- 2}{63}$

Step 3.2.1.2

Divide $x^{3}$ by $1$ .

$x^{3} = \frac{- 2}{63}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x^{3} = - \frac{2}{63}$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{- \frac{2}{63}}$

Step 5

Simplify $\sqrt[3]{- \frac{2}{63}}$ .

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Step 5.1

Rewrite $- \frac{2}{63}$ as ${({(- 1)}^{3})}^{3} \frac{2}{63}$ .

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Step 5.1.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$x = \sqrt[3]{{(- 1)}^{3} \frac{2}{63}}$

Step 5.1.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$x = \sqrt[3]{{({(- 1)}^{3})}^{3} \frac{2}{63}}$

Step 5.2

Pull terms out from under the radical.

$x = {(- 1)}^{3} \sqrt[3]{\frac{2}{63}}$

Step 5.3

Raise $- 1$ to the power of $3$ .

$x = - \sqrt[3]{\frac{2}{63}}$

Step 5.4

Rewrite $\sqrt[3]{\frac{2}{63}}$ as $\frac{\sqrt[3]{2}}{\sqrt[3]{63}}$ .

$x = - \frac{\sqrt[3]{2}}{\sqrt[3]{63}}$

Step 5.5

Multiply $\frac{\sqrt[3]{2}}{\sqrt[3]{63}}$ by $\frac{{\sqrt[3]{63}}^{2}}{{\sqrt[3]{63}}^{2}}$ .

$x = - (\frac{\sqrt[3]{2}}{\sqrt[3]{63}} \cdot \frac{{\sqrt[3]{63}}^{2}}{{\sqrt[3]{63}}^{2}})$

Step 5.6

Combine and simplify the denominator.

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Step 5.6.1

Multiply $\frac{\sqrt[3]{2}}{\sqrt[3]{63}}$ by $\frac{{\sqrt[3]{63}}^{2}}{{\sqrt[3]{63}}^{2}}$ .

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{\sqrt[3]{63} {\sqrt[3]{63}}^{2}}$

Step 5.6.2

Raise $\sqrt[3]{63}$ to the power of $1$ .

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{{\sqrt[3]{63}}^{1} {\sqrt[3]{63}}^{2}}$

Step 5.6.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{{\sqrt[3]{63}}^{1 + 2}}$

Step 5.6.4

Add $1$ and $2$ .

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{{\sqrt[3]{63}}^{3}}$

Step 5.6.5

Rewrite ${\sqrt[3]{63}}^{3}$ as $63$ .

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Step 5.6.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{63}$ as $63^{\frac{1}{3}}$ .

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{{(63^{\frac{1}{3}})}^{3}}$

Step 5.6.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{63^{\frac{1}{3} \cdot 3}}$

Step 5.6.5.3

Combine $\frac{1}{3}$ and $3$ .

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{63^{\frac{3}{3}}}$

Step 5.6.5.4

Cancel the common factor of $3$ .

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Step 5.6.5.4.1

Cancel the common factor.

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{63^{\frac{3}{3}}}$

Step 5.6.5.4.2

Rewrite the expression.

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{63^{1}}$

Step 5.6.5.5

Evaluate the exponent.

$x = - \frac{\sqrt[3]{2} {\sqrt[3]{63}}^{2}}{63}$

Step 5.7

Simplify the numerator.

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Step 5.7.1

Rewrite ${\sqrt[3]{63}}^{2}$ as $\sqrt[3]{63^{2}}$ .

$x = - \frac{\sqrt[3]{2} \sqrt[3]{63^{2}}}{63}$

Step 5.7.2

Raise $63$ to the power of $2$ .

$x = - \frac{\sqrt[3]{2} \sqrt[3]{3969}}{63}$

Step 5.7.3

Rewrite $3969$ as $3^{3} \cdot 147$ .

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Step 5.7.3.1

Factor $27$ out of $3969$ .

$x = - \frac{\sqrt[3]{2} \sqrt[3]{27 (147)}}{63}$

Step 5.7.3.2

Rewrite $27$ as $3^{3}$ .

$x = - \frac{\sqrt[3]{2} \sqrt[3]{3^{3} \cdot 147}}{63}$

Step 5.7.4

Pull terms out from under the radical.

$x = - \frac{\sqrt[3]{2} \cdot 3 \sqrt[3]{147}}{63}$

Step 5.7.5

Combine exponents.

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Step 5.7.5.1

Combine using the product rule for radicals.

$x = - \frac{3 \sqrt[3]{2 \cdot 147}}{63}$

Step 5.7.5.2

Multiply $2$ by $147$ .

$x = - \frac{3 \sqrt[3]{294}}{63}$

Step 5.8

Cancel the common factor of $3$ and $63$ .

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Step 5.8.1

Factor $3$ out of $3 \sqrt[3]{294}$ .

$x = - \frac{3 (\sqrt[3]{294})}{63}$

Step 5.8.2

Cancel the common factors.

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Step 5.8.2.1

Factor $3$ out of $63$ .

$x = - \frac{3 \sqrt[3]{294}}{3 \cdot 21}$

Step 5.8.2.2

Cancel the common factor.

$x = - \frac{3 \sqrt[3]{294}}{3 \cdot 21}$

Step 5.8.2.3

Rewrite the expression.

$x = - \frac{\sqrt[3]{294}}{21}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\sqrt[3]{294}}{21}$

Decimal Form:

$x = - 0.31663808 \dots$