Finite Math Examples

$\sqrt{2 x} + 10 = 4$

Step 1

Subtract $4$ from both sides of the equation.

$\sqrt{2 x} + 10 - 4 = 0$

Step 2

Subtract $4$ from $10$ .

$\sqrt{2 x} + 6 = 0$

Step 3

Subtract $6$ from both sides of the equation.

$\sqrt{2 x} = - 6$

Step 4

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

${\sqrt{2 x}}^{2} = {(- 6)}^{2}$

Step 5

Simplify each side of the equation.

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Step 5.1

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

${({(2 x)}^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

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

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Step 5.2.1.1

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

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Step 5.2.1.1.1

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

${(2 x)}^{\frac{1}{2} \cdot 2} = {(- 6)}^{2}$

Step 5.2.1.1.2

Cancel the common factor of $2$ .

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Step 5.2.1.1.2.1

Cancel the common factor.

${(2 x)}^{\frac{1}{2} \cdot 2} = {(- 6)}^{2}$

Step 5.2.1.1.2.2

Rewrite the expression.

${(2 x)}^{1} = {(- 6)}^{2}$

Step 5.2.1.2

Simplify.

$2 x = {(- 6)}^{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Raise $- 6$ to the power of $2$ .

$2 x = 36$

Step 6

Divide each term in $2 x = 36$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 x = 36$ by $2$ .

$\frac{2 x}{2} = \frac{36}{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{36}{2}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{36}{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $36$ by $2$ .

$x = 18$

Step 7

Exclude the solutions that do not make $\sqrt{2 x} + 6 = 0$ true.

$No solution$