Basic Math Examples

$(a + 1) (a + 5) = - 1$

Step 1

Simplify $(a + 1) (a + 5)$ .

Tap for more steps...

Step 1.1

Expand $(a + 1) (a + 5)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$a (a + 5) + 1 (a + 5) = - 1$

Step 1.1.2

Apply the distributive property.

$a \cdot a + a \cdot 5 + 1 (a + 5) = - 1$

Step 1.1.3

Apply the distributive property.

$a \cdot a + a \cdot 5 + 1 a + 1 \cdot 5 = - 1$

Step 1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.2.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1

Multiply $a$ by $a$ .

$a^{2} + a \cdot 5 + 1 a + 1 \cdot 5 = - 1$

Step 1.2.1.2

Move $5$ to the left of $a$ .

$a^{2} + 5 \cdot a + 1 a + 1 \cdot 5 = - 1$

Step 1.2.1.3

Multiply $a$ by $1$ .

$a^{2} + 5 a + a + 1 \cdot 5 = - 1$

Step 1.2.1.4

Multiply $5$ by $1$ .

$a^{2} + 5 a + a + 5 = - 1$

Step 1.2.2

Add $5 a$ and $a$ .

$a^{2} + 6 a + 5 = - 1$

Step 2

Move all terms to the left side of the equation and simplify.

Tap for more steps...

Step 2.1

Add $1$ to both sides of the equation.

$a^{2} + 6 a + 5 + 1 = 0$

Step 2.2

Add $5$ and $1$ .

$a^{2} + 6 a + 6 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 1$ , $b = 6$ , and $c = 6$ into the quadratic formula and solve for $a$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (1 \cdot 6)}}{2 \cdot 1}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Raise $6$ to the power of $2$ .

$a = \frac{- 6 \pm \sqrt{36 - 4 \cdot 1 \cdot 6}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot 6$ .

Tap for more steps...

Step 5.1.2.1

Multiply $- 4$ by $1$ .

$a = \frac{- 6 \pm \sqrt{36 - 4 \cdot 6}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $6$ .

$a = \frac{- 6 \pm \sqrt{36 - 24}}{2 \cdot 1}$

Step 5.1.3

Subtract $24$ from $36$ .

$a = \frac{- 6 \pm \sqrt{12}}{2 \cdot 1}$

Step 5.1.4

Rewrite $12$ as $2^{2} \cdot 3$ .

Tap for more steps...

Step 5.1.4.1

Factor $4$ out of $12$ .

$a = \frac{- 6 \pm \sqrt{4 (3)}}{2 \cdot 1}$

Step 5.1.4.2

Rewrite $4$ as $2^{2}$ .

$a = \frac{- 6 \pm \sqrt{2^{2} \cdot 3}}{2 \cdot 1}$

Step 5.1.5

Pull terms out from under the radical.

$a = \frac{- 6 \pm 2 \sqrt{3}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$a = \frac{- 6 \pm 2 \sqrt{3}}{2}$

Step 5.3

Simplify $\frac{- 6 \pm 2 \sqrt{3}}{2}$ .

$a = - 3 \pm \sqrt{3}$

Step 6

The final answer is the combination of both solutions.

$a = - 3 + \sqrt{3}, - 3 - \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = - 3 + \sqrt{3}, - 3 - \sqrt{3}$

Decimal Form:

$a = - 1.26794919 \dots, - 4.73205080 \dots$