Solve Using the Quadratic Formula (a+1)(a+2)=0

$(a + 1) (a + 2) = 0$

Step 1

Simplify the left side.

Simplify $(a + 1) (a + 2)$ .

Expand $(a + 1) (a + 2)$ using the FOIL Method.

Apply the distributive property.

$a (a + 2) + 1 (a + 2) = 0$

Apply the distributive property.

$a \cdot a + a \cdot 2 + 1 (a + 2) = 0$

Apply the distributive property.

$a \cdot a + a \cdot 2 + 1 a + 1 \cdot 2 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

$a^{2} + a \cdot 2 + 1 a + 1 \cdot 2 = 0$

Move $2$ to the left of $a$ .

$a^{2} + 2 \cdot a + 1 a + 1 \cdot 2 = 0$

Multiply $a$ by $1$ .

$a^{2} + 2 a + a + 1 \cdot 2 = 0$

Multiply $2$ by $1$ .

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

Add $2 a$ and $a$ .

$a^{2} + 3 a + 2 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 3$ , and $c = 2$ into the quadratic formula and solve for $a$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (1 \cdot 2)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$a = \frac{- 3 \pm \sqrt{9 - 4 \cdot 1 \cdot 2}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 2$ .

Multiply $- 4$ by $1$ .

$a = \frac{- 3 \pm \sqrt{9 - 4 \cdot 2}}{2 \cdot 1}$

Multiply $- 4$ by $2$ .

$a = \frac{- 3 \pm \sqrt{9 - 8}}{2 \cdot 1}$

Subtract $8$ from $9$ .

$a = \frac{- 3 \pm \sqrt{1}}{2 \cdot 1}$

Any root of $1$ is $1$ .

$a = \frac{- 3 \pm 1}{2 \cdot 1}$

Multiply $2$ by $1$ .

$a = \frac{- 3 \pm 1}{2}$

Step 5

The final answer is the combination of both solutions.

$a = - 1, - 2$

Solve Using the Quadratic Formula (a+1)(a+2)=0

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