Finite Math Examples

$(a + 36) (a + 64) = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify $(a + 36) (a + 64)$ .

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Step 1.1.1

Expand $(a + 36) (a + 64)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

$a (a + 64) + 36 (a + 64) = 0$

Step 1.1.1.2

Apply the distributive property.

$a \cdot a + a \cdot 64 + 36 (a + 64) = 0$

Step 1.1.1.3

Apply the distributive property.

$a \cdot a + a \cdot 64 + 36 a + 36 \cdot 64 = 0$

Step 1.1.2

Simplify and combine like terms.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

Multiply $a$ by $a$ .

$a^{2} + a \cdot 64 + 36 a + 36 \cdot 64 = 0$

Step 1.1.2.1.2

Move $64$ to the left of $a$ .

$a^{2} + 64 \cdot a + 36 a + 36 \cdot 64 = 0$

Step 1.1.2.1.3

Multiply $36$ by $64$ .

$a^{2} + 64 a + 36 a + 2304 = 0$

Step 1.1.2.2

Add $64 a$ and $36 a$ .

$a^{2} + 100 a + 2304 = 0$

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 $a = 1$ , $b = 100$ , and $c = 2304$ into the quadratic formula and solve for $a$ .

$\frac{- 100 \pm \sqrt{100^{2} - 4 \cdot (1 \cdot 2304)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $100$ to the power of $2$ .

$a = \frac{- 100 \pm \sqrt{10000 - 4 \cdot 1 \cdot 2304}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot 2304$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$a = \frac{- 100 \pm \sqrt{10000 - 4 \cdot 2304}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $2304$ .

$a = \frac{- 100 \pm \sqrt{10000 - 9216}}{2 \cdot 1}$

Step 4.1.3

Subtract $9216$ from $10000$ .

$a = \frac{- 100 \pm \sqrt{784}}{2 \cdot 1}$

Step 4.1.4

Rewrite $784$ as $28^{2}$ .

$a = \frac{- 100 \pm \sqrt{28^{2}}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$a = \frac{- 100 \pm 28}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$a = \frac{- 100 \pm 28}{2}$

Step 4.3

Simplify $\frac{- 100 \pm 28}{2}$ .

$a = - 50 \pm 14$

Step 5

The final answer is the combination of both solutions.

$a = - 36, - 64$