Finite Math Examples

$4 x^{2} + 16 + 185$

Step 1

Set $4 x^{2} + 16 + 185$ equal to $0$ .

$4 x^{2} + 16 + 185 = 0$

Step 2

Simplify the left side.

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Step 2.1

Add $16$ and $185$ .

$4 x^{2} + 201 = 0$

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 $a = 4$ , $b = 0$ , and $c = 201$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (4 \cdot 201)}}{2 \cdot 4}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 4 \cdot 201}}{2 \cdot 4}$

Step 5.1.2

Multiply $- 4 \cdot 4 \cdot 201$ .

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Step 5.1.2.1

Multiply $- 4$ by $4$ .

$x = \frac{0 \pm \sqrt{0 - 16 \cdot 201}}{2 \cdot 4}$

Step 5.1.2.2

Multiply $- 16$ by $201$ .

$x = \frac{0 \pm \sqrt{0 - 3216}}{2 \cdot 4}$

Step 5.1.3

Subtract $3216$ from $0$ .

$x = \frac{0 \pm \sqrt{- 3216}}{2 \cdot 4}$

Step 5.1.4

Rewrite $- 3216$ as $- 1 (3216)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 3216}}{2 \cdot 4}$

Step 5.1.5

Rewrite $\sqrt{- 1 (3216)}$ as $\sqrt{- 1} \cdot \sqrt{3216}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{3216}}{2 \cdot 4}$

Step 5.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{0 \pm i \cdot \sqrt{3216}}{2 \cdot 4}$

Step 5.1.7

Rewrite $3216$ as $4^{2} \cdot 201$ .

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Step 5.1.7.1

Factor $16$ out of $3216$ .

$x = \frac{0 \pm i \cdot \sqrt{16 (201)}}{2 \cdot 4}$

Step 5.1.7.2

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{4^{2} \cdot 201}}{2 \cdot 4}$

Step 5.1.8

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (4 \sqrt{201})}{2 \cdot 4}$

Step 5.1.9

Move $4$ to the left of $i$ .

$x = \frac{0 \pm 4 i \sqrt{201}}{2 \cdot 4}$

Step 5.2

Multiply $2$ by $4$ .

$x = \frac{0 \pm 4 i \sqrt{201}}{8}$

Step 5.3

Simplify $\frac{0 \pm 4 i \sqrt{201}}{8}$ .

$x = \frac{\pm i \sqrt{201}}{2}$