Trigonometry Examples

$\sqrt{5 x + 2} - 3 = 0$

Step 1

Add $3$ to both sides of the equation.

$\sqrt{5 x + 2} = 3$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{5 x + 2}}^{2} = 3^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x + 2}$ as ${(5 x + 2)}^{\frac{1}{2}}$ .

${({(5 x + 2)}^{\frac{1}{2}})}^{2} = 3^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(5 x + 2)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(5 x + 2)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(5 x + 2)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(5 x + 2)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(5 x + 2)}^{1} = 3^{2}$

Step 3.2.1.2

Simplify.

$5 x + 2 = 3^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $3$ to the power of $2$ .

$5 x + 2 = 9$

Step 4

Solve for $x$ .

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Step 4.1

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1.1

Subtract $2$ from both sides of the equation.

$5 x = 9 - 2$

Step 4.1.2

Subtract $2$ from $9$ .

$5 x = 7$

Step 4.2

Divide each term in $5 x = 7$ by $5$ and simplify.

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Step 4.2.1

Divide each term in $5 x = 7$ by $5$ .

$\frac{5 x}{5} = \frac{7}{5}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{7}{5}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{5}$

Decimal Form:

$x = 1.4$

Mixed Number Form:

$x = 1 \frac{2}{5}$