Finite Math Examples

$100 = 12.1 \sqrt{x}$

Step 1

Rewrite the equation as $12.1 \sqrt{x} = 100$ .

$12.1 \sqrt{x} = 100$

Step 2

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

${(12.1 \sqrt{x})}^{2} = 100^{2}$

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

${(12.1 x^{\frac{1}{2}})}^{2} = 100^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(12.1 x^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $12.1 x^{\frac{1}{2}}$ .

${12.1}^{2} {(x^{\frac{1}{2}})}^{2} = 100^{2}$

Step 3.2.1.2

Raise $12.1$ to the power of $2$ .

$146.41 {(x^{\frac{1}{2}})}^{2} = 100^{2}$

Step 3.2.1.3

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

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Step 3.2.1.3.1

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

$146.41 x^{\frac{1}{2} \cdot 2} = 100^{2}$

Step 3.2.1.3.2

Cancel the common factor of $2$ .

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Step 3.2.1.3.2.1

Cancel the common factor.

$146.41 x^{\frac{1}{2} \cdot 2} = 100^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$146.41 x^{1} = 100^{2}$

Step 3.2.1.4

Simplify.

$146.41 x = 100^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $100$ to the power of $2$ .

$146.41 x = 10000$

Step 4

Divide each term in $146.41 x = 10000$ by $146.41$ and simplify.

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Step 4.1

Divide each term in $146.41 x = 10000$ by $146.41$ .

$\frac{146.41 x}{146.41} = \frac{10000}{146.41}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $146.41$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{146.41 x}{146.41} = \frac{10000}{146.41}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{10000}{146.41}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $10000$ by $146.41$ .

$x = 68.30134553$