Solve for a a^2+2a=15

$a^{2} + 2 a = 15$

Step 1

Subtract $15$ from both sides of the equation.

$a^{2} + 2 a - 15 = 0$

Step 2

Factor $a^{2} + 2 a - 15$ using the AC method.

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 $- 15$ and whose sum is $2$ .

$- 3, 5$

Write the factored form using these integers.

$(a - 3) (a + 5) = 0$

Step 3

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

$a - 3 = 0$

$a + 5 = 0$

Step 4

Set $a - 3$ equal to $0$ and solve for $a$ .

Set $a - 3$ equal to $0$ .

$a - 3 = 0$

Add $3$ to both sides of the equation.

$a = 3$

Step 5

Set $a + 5$ equal to $0$ and solve for $a$ .

Set $a + 5$ equal to $0$ .

$a + 5 = 0$

Subtract $5$ from both sides of the equation.

$a = - 5$

Step 6

The final solution is all the values that make $(a - 3) (a + 5) = 0$ true.

$a = 3, - 5$

Solve for a a^2+2a=15

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