Finite Math Examples

$a^{2} + 16 a + 63$

Step 1

Set $a^{2} + 16 a + 63$ equal to $0$ .

$a^{2} + 16 a + 63 = 0$

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 $a = 1$ , $b = 16$ , and $c = 63$ into the quadratic formula and solve for $a$ .

$\frac{- 16 \pm \sqrt{16^{2} - 4 \cdot (1 \cdot 63)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $16$ to the power of $2$ .

$a = \frac{- 16 \pm \sqrt{256 - 4 \cdot 1 \cdot 63}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot 63$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$a = \frac{- 16 \pm \sqrt{256 - 4 \cdot 63}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $63$ .

$a = \frac{- 16 \pm \sqrt{256 - 252}}{2 \cdot 1}$

Step 4.1.3

Subtract $252$ from $256$ .

$a = \frac{- 16 \pm \sqrt{4}}{2 \cdot 1}$

Step 4.1.4

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

$a = \frac{- 16 \pm \sqrt{2^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$a = \frac{- 16 \pm 2}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$a = \frac{- 16 \pm 2}{2}$

Step 4.3

Simplify $\frac{- 16 \pm 2}{2}$ .

$a = - 8 \pm 1$

Step 5

The final answer is the combination of both solutions.

$a = - 7, - 9$