Pre-Algebra Examples

$9 b^{2} - 6 = 408$

Step 1

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

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Step 1.1

Add $6$ to both sides of the equation.

$9 b^{2} = 408 + 6$

Step 1.2

Add $408$ and $6$ .

$9 b^{2} = 414$

Step 2

Divide each term in $9 b^{2} = 414$ by $9$ and simplify.

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Step 2.1

Divide each term in $9 b^{2} = 414$ by $9$ .

$\frac{9 b^{2}}{9} = \frac{414}{9}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{9 b^{2}}{9} = \frac{414}{9}$

Step 2.2.1.2

Divide $b^{2}$ by $1$ .

$b^{2} = \frac{414}{9}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $414$ by $9$ .

$b^{2} = 46$

Step 3

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

$b = \pm \sqrt{46}$

Step 4

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

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Step 4.1

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

$b = \sqrt{46}$

Step 4.2

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

$b = - \sqrt{46}$

Step 4.3

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

$b = \sqrt{46}, - \sqrt{46}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = \sqrt{46}, - \sqrt{46}$

Decimal Form:

$b = 6.78232998 \dots, - 6.78232998 \dots$