Finite Math Examples

$x^{2} - 40 x + 620$

Step 1

Set $x^{2} - 40 x + 620$ equal to $0$ .

$x^{2} - 40 x + 620 = 0$

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 $a = 1$ , $b = - 40$ , and $c = 620$ into the quadratic formula and solve for $x$ .

$\frac{40 \pm \sqrt{{(- 40)}^{2} - 4 \cdot (1 \cdot 620)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 40$ to the power of $2$ .

$x = \frac{40 \pm \sqrt{1600 - 4 \cdot 1 \cdot 620}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot 620$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{40 \pm \sqrt{1600 - 4 \cdot 620}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $620$ .

$x = \frac{40 \pm \sqrt{1600 - 2480}}{2 \cdot 1}$

Step 4.1.3

Subtract $2480$ from $1600$ .

$x = \frac{40 \pm \sqrt{- 880}}{2 \cdot 1}$

Step 4.1.4

Rewrite $- 880$ as $- 1 (880)$ .

$x = \frac{40 \pm \sqrt{- 1 \cdot 880}}{2 \cdot 1}$

Step 4.1.5

Rewrite $\sqrt{- 1 (880)}$ as $\sqrt{- 1} \cdot \sqrt{880}$ .

$x = \frac{40 \pm \sqrt{- 1} \cdot \sqrt{880}}{2 \cdot 1}$

Step 4.1.6

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

$x = \frac{40 \pm i \cdot \sqrt{880}}{2 \cdot 1}$

Step 4.1.7

Rewrite $880$ as $4^{2} \cdot 55$ .

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Step 4.1.7.1

Factor $16$ out of $880$ .

$x = \frac{40 \pm i \cdot \sqrt{16 (55)}}{2 \cdot 1}$

Step 4.1.7.2

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

$x = \frac{40 \pm i \cdot \sqrt{4^{2} \cdot 55}}{2 \cdot 1}$

Step 4.1.8

Pull terms out from under the radical.

$x = \frac{40 \pm i \cdot (4 \sqrt{55})}{2 \cdot 1}$

Step 4.1.9

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

$x = \frac{40 \pm 4 i \sqrt{55}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{40 \pm 4 i \sqrt{55}}{2}$

Step 4.3

Simplify $\frac{40 \pm 4 i \sqrt{55}}{2}$ .

$x = 20 \pm 2 i \sqrt{55}$