Trigonometry Examples

$8 + \sqrt{2 x} = 5$

Step 1

Move all terms not containing $\sqrt{2 x}$ to the right side of the equation.

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Step 1.1

Subtract $8$ from both sides of the equation.

$\sqrt{2 x} = 5 - 8$

Step 1.2

Subtract $8$ from $5$ .

$\sqrt{2 x} = - 3$

Step 2

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

${\sqrt{2 x}}^{2} = {(- 3)}^{2}$

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 $\sqrt{2 x}$ as ${(2 x)}^{\frac{1}{2}}$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

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

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.

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

Step 3.2.1.1.2.2

Rewrite the expression.

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

Step 3.2.1.2

Simplify.

$2 x = {(- 3)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$2 x = 9$

Step 4

Divide each term in $2 x = 9$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 x = 9$ by $2$ .

$\frac{2 x}{2} = \frac{9}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{9}{2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{2}$

Step 5

Exclude the solutions that do not make $8 + \sqrt{2 x} = 5$ true.

$No solution$