Algebra Examples

$- 4 + 3 b^{2} = 143$

Step 1

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

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Step 1.1

Add $4$ to both sides of the equation.

$3 b^{2} = 143 + 4$

Step 1.2

Add $143$ and $4$ .

$3 b^{2} = 147$

Step 2

Divide each term in $3 b^{2} = 147$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 b^{2} = 147$ by $3$ .

$\frac{3 b^{2}}{3} = \frac{147}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 b^{2}}{3} = \frac{147}{3}$

Step 2.2.1.2

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

$b^{2} = \frac{147}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $147$ by $3$ .

$b^{2} = 49$

Step 3

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

$b = \pm \sqrt{49}$

Step 4

Simplify $\pm \sqrt{49}$ .

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Step 4.1

Rewrite $49$ as $7^{2}$ .

$b = \pm \sqrt{7^{2}}$

Step 4.2

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

$b = \pm 7$

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.

$b = 7$

Step 5.2

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

$b = - 7$

Step 5.3

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

$b = 7, - 7$