Finite Math Examples

$64 x^{2} + 0 x - 10 = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify $64 x^{2} + 0 x - 10$ .

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Step 1.1.1

Multiply $0$ by $x$ .

$64 x^{2} + 0 - 10 = 0$

Step 1.1.2

Add $64 x^{2}$ and $0$ .

$64 x^{2} - 10 = 0$

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 $a = 64$ , $b = 0$ , and $c = - 10$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (64 \cdot - 10)}}{2 \cdot 64}$

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 $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 64 \cdot - 10}}{2 \cdot 64}$

Step 4.1.2

Multiply $- 4 \cdot 64 \cdot - 10$ .

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Step 4.1.2.1

Multiply $- 4$ by $64$ .

$x = \frac{0 \pm \sqrt{0 - 256 \cdot - 10}}{2 \cdot 64}$

Step 4.1.2.2

Multiply $- 256$ by $- 10$ .

$x = \frac{0 \pm \sqrt{0 + 2560}}{2 \cdot 64}$

Step 4.1.3

Add $0$ and $2560$ .

$x = \frac{0 \pm \sqrt{2560}}{2 \cdot 64}$

Step 4.1.4

Rewrite $2560$ as $16^{2} \cdot 10$ .

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Step 4.1.4.1

Factor $256$ out of $2560$ .

$x = \frac{0 \pm \sqrt{256 (10)}}{2 \cdot 64}$

Step 4.1.4.2

Rewrite $256$ as $16^{2}$ .

$x = \frac{0 \pm \sqrt{16^{2} \cdot 10}}{2 \cdot 64}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{0 \pm 16 \sqrt{10}}{2 \cdot 64}$

Step 4.2

Multiply $2$ by $64$ .

$x = \frac{0 \pm 16 \sqrt{10}}{128}$

Step 4.3

Simplify $\frac{0 \pm 16 \sqrt{10}}{128}$ .

$x = \frac{\pm \sqrt{10}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\pm \sqrt{10}}{8}$

Decimal Form:

$x = 0.39528470 \dots, - 0.39528470 \dots$