Basic Math Examples

${(b - 2)}^{2} + b^{2} = 10^{2}$

Step 1

Raise $10$ to the power of $2$ .

${(b - 2)}^{2} + b^{2} = 100$

Step 2

Subtract $100$ from both sides of the equation.

${(b - 2)}^{2} + b^{2} - 100 = 0$

Step 3

Simplify ${(b - 2)}^{2} + b^{2} - 100$ .

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Rewrite ${(b - 2)}^{2}$ as $(b - 2) (b - 2)$ .

$(b - 2) (b - 2) + b^{2} - 100 = 0$

Step 3.1.2

Expand $(b - 2) (b - 2)$ using the FOIL Method.

Tap for more steps...

Step 3.1.2.1

Apply the distributive property.

$b (b - 2) - 2 (b - 2) + b^{2} - 100 = 0$

Step 3.1.2.2

Apply the distributive property.

$b \cdot b + b \cdot - 2 - 2 (b - 2) + b^{2} - 100 = 0$

Step 3.1.2.3

Apply the distributive property.

$b \cdot b + b \cdot - 2 - 2 b - 2 \cdot - 2 + b^{2} - 100 = 0$

Step 3.1.3

Simplify and combine like terms.

Tap for more steps...

Step 3.1.3.1

Simplify each term.

Tap for more steps...

Step 3.1.3.1.1

Multiply $b$ by $b$ .

$b^{2} + b \cdot - 2 - 2 b - 2 \cdot - 2 + b^{2} - 100 = 0$

Step 3.1.3.1.2

Move $- 2$ to the left of $b$ .

$b^{2} - 2 \cdot b - 2 b - 2 \cdot - 2 + b^{2} - 100 = 0$

Step 3.1.3.1.3

Multiply $- 2$ by $- 2$ .

$b^{2} - 2 b - 2 b + 4 + b^{2} - 100 = 0$

Step 3.1.3.2

Subtract $2 b$ from $- 2 b$ .

$b^{2} - 4 b + 4 + b^{2} - 100 = 0$

Step 3.2

Add $b^{2}$ and $b^{2}$ .

$2 b^{2} - 4 b + 4 - 100 = 0$

Step 3.3

Subtract $100$ from $4$ .

$2 b^{2} - 4 b - 96 = 0$

Step 4

Factor the left side of the equation.

Tap for more steps...

Step 4.1

Factor $2$ out of $2 b^{2} - 4 b - 96$ .

Tap for more steps...

Step 4.1.1

Factor $2$ out of $2 b^{2}$ .

$2 (b^{2}) - 4 b - 96 = 0$

Step 4.1.2

Factor $2$ out of $- 4 b$ .

$2 (b^{2}) + 2 (- 2 b) - 96 = 0$

Step 4.1.3

Factor $2$ out of $- 96$ .

$2 b^{2} + 2 (- 2 b) + 2 \cdot - 48 = 0$

Step 4.1.4

Factor $2$ out of $2 b^{2} + 2 (- 2 b)$ .

$2 (b^{2} - 2 b) + 2 \cdot - 48 = 0$

Step 4.1.5

Factor $2$ out of $2 (b^{2} - 2 b) + 2 \cdot - 48$ .

$2 (b^{2} - 2 b - 48) = 0$

Step 4.2

Factor.

Tap for more steps...

Step 4.2.1

Factor $b^{2} - 2 b - 48$ using the AC method.

Tap for more steps...

Step 4.2.1.1

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 $- 48$ and whose sum is $- 2$ .

$- 8, 6$

Step 4.2.1.2

Write the factored form using these integers.

$2 ((b - 8) (b + 6)) = 0$

Step 4.2.2

Remove unnecessary parentheses.

$2 (b - 8) (b + 6) = 0$

Step 5

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

$b - 8 = 0$

$b + 6 = 0$

Step 6

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

Tap for more steps...

Step 6.1

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

$b - 8 = 0$

Step 6.2

Add $8$ to both sides of the equation.

$b = 8$

Step 7

Set $b + 6$ equal to $0$ and solve for $b$ .

Tap for more steps...

Step 7.1

Set $b + 6$ equal to $0$ .

$b + 6 = 0$

Step 7.2

Subtract $6$ from both sides of the equation.

$b = - 6$

Step 8

The final solution is all the values that make $2 (b - 8) (b + 6) = 0$ true.

$b = 8, - 6$