Basic Math Examples

$56 = a + a^{2}$

Step 1

Rewrite the equation as $a + a^{2} = 56$ .

$a + a^{2} = 56$

Step 2

Subtract $56$ from both sides of the equation.

$a + a^{2} - 56 = 0$

Step 3

Factor the left side of the equation.

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Step 3.1

Let $u = a$ . Substitute $u$ for all occurrences of $a$ .

$u + u^{2} - 56 = 0$

Step 3.2

Factor $u + u^{2} - 56$ using the AC method.

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Step 3.2.1

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 $- 56$ and whose sum is $1$ .

$- 7, 8$

Step 3.2.2

Write the factored form using these integers.

$(u - 7) (u + 8) = 0$

Step 3.3

Replace all occurrences of $u$ with $a$ .

$(a - 7) (a + 8) = 0$

Step 4

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

$a - 7 = 0$

$a + 8 = 0$

Step 5

Set $a - 7$ equal to $0$ and solve for $a$ .

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Step 5.1

Set $a - 7$ equal to $0$ .

$a - 7 = 0$

Step 5.2

Add $7$ to both sides of the equation.

$a = 7$

Step 6

Set $a + 8$ equal to $0$ and solve for $a$ .

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Step 6.1

Set $a + 8$ equal to $0$ .

$a + 8 = 0$

Step 6.2

Subtract $8$ from both sides of the equation.

$a = - 8$

Step 7

The final solution is all the values that make $(a - 7) (a + 8) = 0$ true.

$a = 7, - 8$