Trigonometry Examples

$- 93 = - 5 \sqrt{u - 53}$

Step 1

Rewrite the equation as $- 5 \sqrt{u - 53} = - 93$ .

$- 5 \sqrt{u - 53} = - 93$

Step 2

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

${(- 5 \sqrt{u - 53})}^{2} = {(- 93)}^{2}$

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 $\sqrt{u - 53}$ as ${(u - 53)}^{\frac{1}{2}}$ .

${(- 5 {(u - 53)}^{\frac{1}{2}})}^{2} = {(- 93)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(- 5 {(u - 53)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $- 5 {(u - 53)}^{\frac{1}{2}}$ .

${(- 5)}^{2} {({(u - 53)}^{\frac{1}{2}})}^{2} = {(- 93)}^{2}$

Step 3.2.1.2

Raise $- 5$ to the power of $2$ .

$25 {({(u - 53)}^{\frac{1}{2}})}^{2} = {(- 93)}^{2}$

Step 3.2.1.3

Multiply the exponents in ${({(u - 53)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.3.1

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

$25 {(u - 53)}^{\frac{1}{2} \cdot 2} = {(- 93)}^{2}$

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.

$25 {(u - 53)}^{\frac{1}{2} \cdot 2} = {(- 93)}^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$25 {(u - 53)}^{1} = {(- 93)}^{2}$

Step 3.2.1.4

Simplify.

$25 (u - 53) = {(- 93)}^{2}$

Step 3.2.1.5

Apply the distributive property.

$25 u + 25 \cdot - 53 = {(- 93)}^{2}$

Step 3.2.1.6

Multiply $25$ by $- 53$ .

$25 u - 1325 = {(- 93)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $- 93$ to the power of $2$ .

$25 u - 1325 = 8649$

Step 4

Solve for $u$ .

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Step 4.1

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

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Step 4.1.1

Add $1325$ to both sides of the equation.

$25 u = 8649 + 1325$

Step 4.1.2

Add $8649$ and $1325$ .

$25 u = 9974$

Step 4.2

Divide each term in $25 u = 9974$ by $25$ and simplify.

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Step 4.2.1

Divide each term in $25 u = 9974$ by $25$ .

$\frac{25 u}{25} = \frac{9974}{25}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $25$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{25 u}{25} = \frac{9974}{25}$

Step 4.2.2.1.2

Divide $u$ by $1$ .

$u = \frac{9974}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$u = \frac{9974}{25}$

Decimal Form:

$u = 398.96$

Mixed Number Form:

$u = 398 \frac{24}{25}$