Basic Math Examples

$24 = \sqrt{j^{2}} - {(22 - 4)}^{2}$

Step 1

Rewrite the equation as $\sqrt{j^{2}} - {(22 - 4)}^{2} = 24$ .

$\sqrt{j^{2}} - {(22 - 4)}^{2} = 24$

Step 2

Solve for $\sqrt{j^{2}}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Subtract $4$ from $22$ .

$\sqrt{j^{2}} - 18^{2} = 24$

Step 2.1.2

Raise $18$ to the power of $2$ .

$\sqrt{j^{2}} - 1 \cdot 324 = 24$

Step 2.1.3

Multiply $- 1$ by $324$ .

$\sqrt{j^{2}} - 324 = 24$

Step 2.2

Move all terms not containing $\sqrt{j^{2}}$ to the right side of the equation.

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Step 2.2.1

Add $324$ to both sides of the equation.

$\sqrt{j^{2}} = 24 + 324$

Step 2.2.2

Add $24$ and $324$ .

$\sqrt{j^{2}} = 348$

Step 3

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

${\sqrt{j^{2}}}^{2} = 348^{2}$

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 $\sqrt{j^{2}}$ as $j^{\frac{2}{2}}$ .

${(j^{\frac{2}{2}})}^{2} = 348^{2}$

Step 4.2

Divide $2$ by $2$ .

${(j^{1})}^{2} = 348^{2}$

Step 4.3

Simplify the left side.

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Step 4.3.1

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

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Step 4.3.1.1

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

$j^{1 \cdot 2} = 348^{2}$

Step 4.3.1.2

Multiply $2$ by $1$ .

$j^{2} = 348^{2}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Raise $348$ to the power of $2$ .

$j^{2} = 121104$

Step 5

Solve for $j$ .

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Step 5.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$j = \pm \sqrt{121104}$

Step 5.2

Simplify $\pm \sqrt{121104}$ .

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Step 5.2.1

Rewrite $121104$ as $348^{2}$ .

$j = \pm \sqrt{348^{2}}$

Step 5.2.2

Pull terms out from under the radical, assuming positive real numbers.

$j = \pm 348$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.3.1

First, use the positive value of the $\pm$ to find the first solution.

$j = 348$

Step 5.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$j = - 348$

Step 5.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$j = 348, - 348$