Finite Math Examples

$x^{2} - 2 x - 49$

Step 1

Set $x^{2} - 2 x - 49$ equal to $0$ .

$x^{2} - 2 x - 49 = 0$

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 $a = 1$ , $b = - 2$ , and $c = - 49$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (1 \cdot - 49)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 49}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 49$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot - 49}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 49$ .

$x = \frac{2 \pm \sqrt{4 + 196}}{2 \cdot 1}$

Step 4.1.3

Add $4$ and $196$ .

$x = \frac{2 \pm \sqrt{200}}{2 \cdot 1}$

Step 4.1.4

Rewrite $200$ as $10^{2} \cdot 2$ .

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Step 4.1.4.1

Factor $100$ out of $200$ .

$x = \frac{2 \pm \sqrt{100 (2)}}{2 \cdot 1}$

Step 4.1.4.2

Rewrite $100$ as $10^{2}$ .

$x = \frac{2 \pm \sqrt{10^{2} \cdot 2}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{2 \pm 10 \sqrt{2}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{2 \pm 10 \sqrt{2}}{2}$

Step 4.3

Simplify $\frac{2 \pm 10 \sqrt{2}}{2}$ .

$x = 1 \pm 5 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 1 \pm 5 \sqrt{2}$

Decimal Form:

$x = 8.07106781 \dots, - 6.07106781 \dots$