Basic Math Examples

$m^{2} + 10 m = - 9$

Step 1

Add $9$ to both sides of the equation.

$m^{2} + 10 m + 9 = 0$

Step 2

Factor $m^{2} + 10 m + 9$ using the AC method.

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Step 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 $9$ and whose sum is $10$ .

$1, 9$

Step 2.2

Write the factored form using these integers.

$(m + 1) (m + 9) = 0$

Step 3

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

$m + 1 = 0$

$m + 9 = 0$

Step 4

Set $m + 1$ equal to $0$ and solve for $m$ .

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Step 4.1

Set $m + 1$ equal to $0$ .

$m + 1 = 0$

Step 4.2

Subtract $1$ from both sides of the equation.

$m = - 1$

Step 5

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

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Step 5.1

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

$m + 9 = 0$

Step 5.2

Subtract $9$ from both sides of the equation.

$m = - 9$

Step 6

The final solution is all the values that make $(m + 1) (m + 9) = 0$ true.

$m = - 1, - 9$