Basic Math Examples

$- {(\sqrt{7})}^{2} + b^{2} = 6^{2}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

$- {(7^{\frac{1}{2}})}^{2} + b^{2} = 6^{2}$

Step 1.1.2

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

$- 7^{\frac{1}{2} \cdot 2} + b^{2} = 6^{2}$

Step 1.1.3

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

$- 7^{\frac{2}{2}} + b^{2} = 6^{2}$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Cancel the common factor.

$- 7^{\frac{2}{2}} + b^{2} = 6^{2}$

Step 1.1.4.2

Rewrite the expression.

$- 7^{1} + b^{2} = 6^{2}$

Step 1.1.5

Evaluate the exponent.

$- 1 \cdot 7 + b^{2} = 6^{2}$

Step 1.2

Multiply $- 1$ by $7$ .

$- 7 + b^{2} = 6^{2}$

Step 2

Raise $6$ to the power of $2$ .

$- 7 + b^{2} = 36$

Step 3

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

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Step 3.1

Add $7$ to both sides of the equation.

$b^{2} = 36 + 7$

Step 3.2

Add $36$ and $7$ .

$b^{2} = 43$

Step 4

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

$b = \pm \sqrt{43}$

Step 5

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

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Step 5.1

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

$b = \sqrt{43}$

Step 5.2

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

$b = - \sqrt{43}$

Step 5.3

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

$b = \sqrt{43}, - \sqrt{43}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$b = \sqrt{43}, - \sqrt{43}$

Decimal Form:

$b = 6.55743852 \dots, - 6.55743852 \dots$