Algebra Examples

$1 = 2 π \sqrt{\frac{x}{9.8}}$

Step 1

Rewrite the equation as $2 π \sqrt{\frac{x}{9.8}} = 1$ .

$2 π \sqrt{\frac{x}{9.8}} = 1$

Step 2

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

${(2 π \sqrt{\frac{x}{9.8}})}^{2} = 1^{2}$

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 $\sqrt{\frac{x}{9.8}}$ as ${(\frac{x}{9.8})}^{\frac{1}{2}}$ .

${(2 π {(\frac{x}{9.8})}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(2 π {(\frac{x}{9.8})}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply by $1$ .

${(2 π {(\frac{1 x}{9.8})}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2.1.2

Factor $9.8$ out of $9.8$ .

${(2 π {(\frac{1 x}{9.8 (1)})}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2.1.3

Separate fractions.

${(2 π {(\frac{1}{9.8} \cdot \frac{x}{1})}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2.1.4

Simplify the expression.

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Step 3.2.1.4.1

Divide $1$ by $9.8$ .

${(2 π {(0.10204081 \frac{x}{1})}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2.1.4.2

Divide $x$ by $1$ .

${(2 π {(0.10204081 x)}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2.1.4.3

Apply the product rule to $0.10204081 x$ .

${(2 π ({0.10204081}^{\frac{1}{2}} x^{\frac{1}{2}}))}^{2} = 1^{2}$

Step 3.2.1.4.4

Rewrite $0.10204081$ as ${0.31943828}^{2}$ .

${(2 π ({({0.31943828}^{2})}^{\frac{1}{2}} x^{\frac{1}{2}}))}^{2} = 1^{2}$

Step 3.2.1.4.5

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

${(2 π ({0.31943828}^{2 (\frac{1}{2})} x^{\frac{1}{2}}))}^{2} = 1^{2}$

Step 3.2.1.5

Cancel the common factor of $2$ .

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Step 3.2.1.5.1

Cancel the common factor.

${(2 π ({0.31943828}^{2 (\frac{1}{2})} x^{\frac{1}{2}}))}^{2} = 1^{2}$

Step 3.2.1.5.2

Rewrite the expression.

${(2 π ({0.31943828}^{1} x^{\frac{1}{2}}))}^{2} = 1^{2}$

Step 3.2.1.6

Evaluate the exponent.

${(2 π (0.31943828 x^{\frac{1}{2}}))}^{2} = 1^{2}$

Step 3.2.1.7

Multiply $2 π (0.31943828 x^{\frac{1}{2}})$ .

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Step 3.2.1.7.1

Multiply $0.31943828$ by $2$ .

${(0.63887656 π x^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2.1.7.2

Multiply $0.63887656$ by $π$ .

${(2.00708992 x^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2.1.8

Apply the product rule to $2.00708992 x^{\frac{1}{2}}$ .

${2.00708992}^{2} {(x^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2.1.9

Raise $2.00708992$ to the power of $2$ .

$4.02840995 {(x^{\frac{1}{2}})}^{2} = 1^{2}$

Step 3.2.1.10

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

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Step 3.2.1.10.1

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

$4.02840995 x^{\frac{1}{2} \cdot 2} = 1^{2}$

Step 3.2.1.10.2

Cancel the common factor of $2$ .

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Step 3.2.1.10.2.1

Cancel the common factor.

$4.02840995 x^{\frac{1}{2} \cdot 2} = 1^{2}$

Step 3.2.1.10.2.2

Rewrite the expression.

$4.02840995 x^{1} = 1^{2}$

Step 3.2.1.11

Simplify.

$4.02840995 x = 1^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

One to any power is one.

$4.02840995 x = 1$

Step 4

Divide each term in $4.02840995 x = 1$ by $4.02840995$ and simplify.

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Step 4.1

Divide each term in $4.02840995 x = 1$ by $4.02840995$ .

$\frac{4.02840995 x}{4.02840995} = \frac{1}{4.02840995}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4.02840995$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4.02840995 x}{4.02840995} = \frac{1}{4.02840995}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{4.02840995}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $1$ by $4.02840995$ .

$x = 0.24823689$