Calculus Examples

$9.3 = 3 {({(\sqrt{7})}^{2} + 3)}^{\frac{2}{3}} + C$

Step 1

Rewrite the equation as $3 {({\sqrt{7}}^{2} + 3)}^{\frac{2}{3}} + C = 9.3$ .

$3 {({\sqrt{7}}^{2} + 3)}^{\frac{2}{3}} + C = 9.3$

Step 2

Simplify each term.

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Step 2.1

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 2.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$3 {({(7^{\frac{1}{2}})}^{2} + 3)}^{\frac{2}{3}} + C = 9.3$

Step 2.1.2

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

$3 {(7^{\frac{1}{2} \cdot 2} + 3)}^{\frac{2}{3}} + C = 9.3$

Step 2.1.3

Combine $\frac{1}{2}$ and $2$ .

$3 {(7^{\frac{2}{2}} + 3)}^{\frac{2}{3}} + C = 9.3$

Step 2.1.4

Cancel the common factor of $2$ .

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Step 2.1.4.1

Cancel the common factor.

$3 {(7^{\frac{2}{2}} + 3)}^{\frac{2}{3}} + C = 9.3$

Step 2.1.4.2

Rewrite the expression.

$3 {(7^{1} + 3)}^{\frac{2}{3}} + C = 9.3$

Step 2.1.5

Evaluate the exponent.

$3 {(7 + 3)}^{\frac{2}{3}} + C = 9.3$

Step 2.2

Add $7$ and $3$ .

$3 \cdot 10^{\frac{2}{3}} + C = 9.3$

Step 3

Move all terms not containing $C$ to the right side of the equation.

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Step 3.1

Subtract $3 \cdot 10^{\frac{2}{3}}$ from both sides of the equation.

$C = 9.3 - 3 \cdot 10^{\frac{2}{3}}$

Step 3.2

Subtract $3 \cdot 10^{\frac{2}{3}}$ from $9.3$ .

$C = - 4.6247665$