Finite Math Examples

$0 = x^{2} - 195 + 8450$

Step 1

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

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Step 1.1

Simplify the right side.

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Step 1.1.1

Add $- 195$ and $8450$ .

$0 = x^{2} + 8255$

Step 1.2

Move all the expressions to the left side of the equation.

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Step 1.2.1

Subtract $x^{2}$ from both sides of the equation.

$- x^{2} = 8255$

Step 1.2.2

Subtract $8255$ from both sides of the equation.

$- x^{2} - 8255 = 0$

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 $a = - 1$ , $b = 0$ , and $c = - 8255$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 1 \cdot - 8255)}}{2 \cdot - 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1 \cdot - 8255}}{2 \cdot - 1}$

Step 4.1.2

Multiply $- 4 \cdot - 1 \cdot - 8255$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 4 \cdot - 8255}}{2 \cdot - 1}$

Step 4.1.2.2

Multiply $4$ by $- 8255$ .

$x = \frac{0 \pm \sqrt{0 - 33020}}{2 \cdot - 1}$

Step 4.1.3

Subtract $33020$ from $0$ .

$x = \frac{0 \pm \sqrt{- 33020}}{2 \cdot - 1}$

Step 4.1.4

Rewrite $- 33020$ as $- 1 (33020)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 33020}}{2 \cdot - 1}$

Step 4.1.5

Rewrite $\sqrt{- 1 (33020)}$ as $\sqrt{- 1} \cdot \sqrt{33020}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{33020}}{2 \cdot - 1}$

Step 4.1.6

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

$x = \frac{0 \pm i \cdot \sqrt{33020}}{2 \cdot - 1}$

Step 4.1.7

Rewrite $33020$ as $2^{2} \cdot 8255$ .

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Step 4.1.7.1

Factor $4$ out of $33020$ .

$x = \frac{0 \pm i \cdot \sqrt{4 (8255)}}{2 \cdot - 1}$

Step 4.1.7.2

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

$x = \frac{0 \pm i \cdot \sqrt{2^{2} \cdot 8255}}{2 \cdot - 1}$

Step 4.1.8

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (2 \sqrt{8255})}{2 \cdot - 1}$

Step 4.1.9

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

$x = \frac{0 \pm 2 i \sqrt{8255}}{2 \cdot - 1}$

Step 4.2

Multiply $2$ by $- 1$ .

$x = \frac{0 \pm 2 i \sqrt{8255}}{- 2}$

Step 4.3

Simplify $\frac{0 \pm 2 i \sqrt{8255}}{- 2}$ .

$x = \pm i \sqrt{8255}$