Finite Math Examples

$3.14 x^{2} + \sqrt{119} - (5 x^{2} - x) + 3$

Step 1

Set $3.14 x^{2} + \sqrt{119} - (5 x^{2} - x) + 3$ equal to $0$ .

$3.14 x^{2} + \sqrt{119} - (5 x^{2} - x) + 3 = 0$

Step 2

Simplify the left side.

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Step 2.1

Simplify $3.14 x^{2} + \sqrt{119} - (5 x^{2} - x) + 3$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$3.14 x^{2} + \sqrt{119} - (5 x^{2}) - - x + 3 = 0$

Step 2.1.1.2

Multiply $5$ by $- 1$ .

$3.14 x^{2} + \sqrt{119} - 5 x^{2} - - x + 3 = 0$

Step 2.1.1.3

Multiply $- - x$ .

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Step 2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$3.14 x^{2} + \sqrt{119} - 5 x^{2} + 1 x + 3 = 0$

Step 2.1.1.3.2

Multiply $x$ by $1$ .

$3.14 x^{2} + \sqrt{119} - 5 x^{2} + x + 3 = 0$

Step 2.1.2

Subtract $5 x^{2}$ from $3.14 x^{2}$ .

$- 1.86 x^{2} + \sqrt{119} + x + 3 = 0$

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 $a = - 1.86$ , $b = 1$ , and $c = \sqrt{119} + 3$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (- 1.86 \cdot (\sqrt{119} + 3))}}{2 \cdot - 1.86}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot - 1.86 \cdot (\sqrt{119} + 3)}}{2 \cdot - 1.86}$

Step 5.1.2

Multiply $- 4$ by $- 1.86$ .

$x = \frac{- 1 \pm \sqrt{1 + 7.44 \cdot (\sqrt{119} + 3)}}{2 \cdot - 1.86}$

Step 5.1.3

Multiply $7.44$ by $\sqrt{119} + 3$ .

$x = \frac{- 1 \pm \sqrt{1 + 103.48081813}}{2 \cdot - 1.86}$

Step 5.1.4

Add $1$ and $103.48081813$ .

$x = \frac{- 1 \pm \sqrt{104.48081813}}{2 \cdot - 1.86}$

Step 5.2

Multiply $2$ by $- 1.86$ .

$x = \frac{- 1 \pm \sqrt{104.48081813}}{- 3.72}$

Step 5.3

Simplify $\frac{- 1 \pm \sqrt{104.48081813}}{- 3.72}$ .

$x = \frac{25 \pm 25 \sqrt{104.48081813}}{93}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25 \pm 25 \sqrt{104.48081813}}{93}$

Decimal Form:

$x = 3.01655534 \dots, - 2.47892093 \dots$