Basic Math Examples

$s = 19 \sqrt{2 t} + 48$

Step 1

Rewrite the equation as $19 \sqrt{2 t} + 48 = s$ .

$19 \sqrt{2 t} + 48 = s$

Step 2

Subtract $48$ from both sides of the equation.

$19 \sqrt{2 t} = s - 48$

Step 3

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

${(19 \sqrt{2 t})}^{2} = {(s - 48)}^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

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

${(19 {(2 t)}^{\frac{1}{2}})}^{2} = {(s - 48)}^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${(19 {(2 t)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

Apply the product rule to $2 t$ .

${(19 (2^{\frac{1}{2}} t^{\frac{1}{2}}))}^{2} = {(s - 48)}^{2}$

Step 4.2.1.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.2.1.2.1

Apply the product rule to $19 \cdot 2^{\frac{1}{2}} t^{\frac{1}{2}}$ .

${(19 \cdot 2^{\frac{1}{2}})}^{2} {(t^{\frac{1}{2}})}^{2} = {(s - 48)}^{2}$

Step 4.2.1.2.2

Apply the product rule to $19 \cdot 2^{\frac{1}{2}}$ .

$19^{2} \cdot {(2^{\frac{1}{2}})}^{2} {(t^{\frac{1}{2}})}^{2} = {(s - 48)}^{2}$

Step 4.2.1.3

Raise $19$ to the power of $2$ .

$361 \cdot {(2^{\frac{1}{2}})}^{2} {(t^{\frac{1}{2}})}^{2} = {(s - 48)}^{2}$

Step 4.2.1.4

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

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Step 4.2.1.4.1

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

$361 \cdot 2^{\frac{1}{2} \cdot 2} {(t^{\frac{1}{2}})}^{2} = {(s - 48)}^{2}$

Step 4.2.1.4.2

Cancel the common factor of $2$ .

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Step 4.2.1.4.2.1

Cancel the common factor.

$361 \cdot 2^{\frac{1}{2} \cdot 2} {(t^{\frac{1}{2}})}^{2} = {(s - 48)}^{2}$

Step 4.2.1.4.2.2

Rewrite the expression.

$361 \cdot 2^{1} {(t^{\frac{1}{2}})}^{2} = {(s - 48)}^{2}$

Step 4.2.1.5

Evaluate the exponent.

$361 \cdot 2 {(t^{\frac{1}{2}})}^{2} = {(s - 48)}^{2}$

Step 4.2.1.6

Multiply $361$ by $2$ .

$722 {(t^{\frac{1}{2}})}^{2} = {(s - 48)}^{2}$

Step 4.2.1.7

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

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Step 4.2.1.7.1

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

$722 t^{\frac{1}{2} \cdot 2} = {(s - 48)}^{2}$

Step 4.2.1.7.2

Cancel the common factor of $2$ .

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Step 4.2.1.7.2.1

Cancel the common factor.

$722 t^{\frac{1}{2} \cdot 2} = {(s - 48)}^{2}$

Step 4.2.1.7.2.2

Rewrite the expression.

$722 t^{1} = {(s - 48)}^{2}$

Step 4.2.1.8

Simplify.

$722 t = {(s - 48)}^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify ${(s - 48)}^{2}$ .

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Step 4.3.1.1

Rewrite ${(s - 48)}^{2}$ as $(s - 48) (s - 48)$ .

$722 t = (s - 48) (s - 48)$

Step 4.3.1.2

Expand $(s - 48) (s - 48)$ using the FOIL Method.

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Step 4.3.1.2.1

Apply the distributive property.

$722 t = s (s - 48) - 48 (s - 48)$

Step 4.3.1.2.2

Apply the distributive property.

$722 t = s \cdot s + s \cdot - 48 - 48 (s - 48)$

Step 4.3.1.2.3

Apply the distributive property.

$722 t = s \cdot s + s \cdot - 48 - 48 s - 48 \cdot - 48$

Step 4.3.1.3

Simplify and combine like terms.

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Step 4.3.1.3.1

Simplify each term.

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Step 4.3.1.3.1.1

Multiply $s$ by $s$ .

$722 t = s^{2} + s \cdot - 48 - 48 s - 48 \cdot - 48$

Step 4.3.1.3.1.2

Move $- 48$ to the left of $s$ .

$722 t = s^{2} - 48 \cdot s - 48 s - 48 \cdot - 48$

Step 4.3.1.3.1.3

Multiply $- 48$ by $- 48$ .

$722 t = s^{2} - 48 s - 48 s + 2304$

Step 4.3.1.3.2

Subtract $48 s$ from $- 48 s$ .

$722 t = s^{2} - 96 s + 2304$

Step 5

Divide each term in $722 t = s^{2} - 96 s + 2304$ by $722$ and simplify.

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Step 5.1

Divide each term in $722 t = s^{2} - 96 s + 2304$ by $722$ .

$\frac{722 t}{722} = \frac{s^{2}}{722} + \frac{- 96 s}{722} + \frac{2304}{722}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $722$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{722 t}{722} = \frac{s^{2}}{722} + \frac{- 96 s}{722} + \frac{2304}{722}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t = \frac{s^{2}}{722} + \frac{- 96 s}{722} + \frac{2304}{722}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Cancel the common factor of $- 96$ and $722$ .

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Step 5.3.1.1.1

Factor $2$ out of $- 96 s$ .

$t = \frac{s^{2}}{722} + \frac{2 (- 48 s)}{722} + \frac{2304}{722}$

Step 5.3.1.1.2

Cancel the common factors.

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Step 5.3.1.1.2.1

Factor $2$ out of $722$ .

$t = \frac{s^{2}}{722} + \frac{2 (- 48 s)}{2 (361)} + \frac{2304}{722}$

Step 5.3.1.1.2.2

Cancel the common factor.

$t = \frac{s^{2}}{722} + \frac{2 (- 48 s)}{2 \cdot 361} + \frac{2304}{722}$

Step 5.3.1.1.2.3

Rewrite the expression.

$t = \frac{s^{2}}{722} + \frac{- 48 s}{361} + \frac{2304}{722}$

Step 5.3.1.2

Move the negative in front of the fraction.

$t = \frac{s^{2}}{722} - \frac{48 s}{361} + \frac{2304}{722}$

Step 5.3.1.3

Cancel the common factor of $2304$ and $722$ .

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Step 5.3.1.3.1

Factor $2$ out of $2304$ .

$t = \frac{s^{2}}{722} - \frac{48 s}{361} + \frac{2 (1152)}{722}$

Step 5.3.1.3.2

Cancel the common factors.

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Step 5.3.1.3.2.1

Factor $2$ out of $722$ .

$t = \frac{s^{2}}{722} - \frac{48 s}{361} + \frac{2 \cdot 1152}{2 \cdot 361}$

Step 5.3.1.3.2.2

Cancel the common factor.

$t = \frac{s^{2}}{722} - \frac{48 s}{361} + \frac{2 \cdot 1152}{2 \cdot 361}$

Step 5.3.1.3.2.3

Rewrite the expression.

$t = \frac{s^{2}}{722} - \frac{48 s}{361} + \frac{1152}{361}$