Basic Math Examples

$36 = \frac{1}{2} \cdot (B (B + 1))$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (B (B + 1)) = 36$ .

$\frac{1}{2} \cdot (B (B + 1)) = 36$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (B (B + 1))) = 2 \cdot 36$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $2 (\frac{1}{2} \cdot (B (B + 1)))$ .

Tap for more steps...

Step 3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} \cdot (B \cdot B + B \cdot 1)) = 2 \cdot 36$

Step 3.1.1.2

Simplify the expression.

Tap for more steps...

Step 3.1.1.2.1

Multiply $B$ by $B$ .

$2 (\frac{1}{2} \cdot (B^{2} + B \cdot 1)) = 2 \cdot 36$

Step 3.1.1.2.2

Multiply $B$ by $1$ .

$2 (\frac{1}{2} \cdot (B^{2} + B)) = 2 \cdot 36$

Step 3.1.1.3

Apply the distributive property.

$2 (\frac{1}{2} B^{2} + \frac{1}{2} B) = 2 \cdot 36$

Step 3.1.1.4

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

$2 (\frac{B^{2}}{2} + \frac{1}{2} B) = 2 \cdot 36$

Step 3.1.1.5

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

$2 (\frac{B^{2}}{2} + \frac{B}{2}) = 2 \cdot 36$

Step 3.1.1.6

Apply the distributive property.

$2 \frac{B^{2}}{2} + 2 \frac{B}{2} = 2 \cdot 36$

Step 3.1.1.7

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1.7.1

Cancel the common factor.

$2 \frac{B^{2}}{2} + 2 \frac{B}{2} = 2 \cdot 36$

Step 3.1.1.7.2

Rewrite the expression.

$B^{2} + 2 \frac{B}{2} = 2 \cdot 36$

Step 3.1.1.8

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1.8.1

Cancel the common factor.

$B^{2} + 2 \frac{B}{2} = 2 \cdot 36$

Step 3.1.1.8.2

Rewrite the expression.

$B^{2} + B = 2 \cdot 36$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $2$ by $36$ .

$B^{2} + B = 72$

Step 4

Subtract $72$ from both sides of the equation.

$B^{2} + B - 72 = 0$

Step 5

Factor $B^{2} + B - 72$ using the AC method.

Tap for more steps...

Step 5.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 72$ and whose sum is $1$ .

$- 8, 9$

Step 5.2

Write the factored form using these integers.

$(B - 8) (B + 9) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$B - 8 = 0$

$B + 9 = 0$

Step 7

Set $B - 8$ equal to $0$ and solve for $B$ .

Tap for more steps...

Step 7.1

Set $B - 8$ equal to $0$ .

$B - 8 = 0$

Step 7.2

Add $8$ to both sides of the equation.

$B = 8$

Step 8

Set $B + 9$ equal to $0$ and solve for $B$ .

Tap for more steps...

Step 8.1

Set $B + 9$ equal to $0$ .

$B + 9 = 0$

Step 8.2

Subtract $9$ from both sides of the equation.

$B = - 9$

Step 9

The final solution is all the values that make $(B - 8) (B + 9) = 0$ true.

$B = 8, - 9$