Solve Using the Quadratic Formula 3x^2+2x-3=0

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Algebra

$3 x^{2} + 2 x - 3 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 3$ , $b = 2$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (3 \cdot - 3)}}{2 \cdot 3}$

Simplify.

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Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 3 \cdot - 3}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{- 2 \pm \sqrt{4 - 12 \cdot - 3}}{2 \cdot 3}$

Multiply $- 12$ by $- 3$ .

$x = \frac{- 2 \pm \sqrt{4 + 36}}{2 \cdot 3}$

Add $4$ and $36$ .

$x = \frac{- 2 \pm \sqrt{40}}{2 \cdot 3}$

Rewrite $40$ as $2^{2} \cdot 10$ .

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Factor $4$ out of $40$ .

$x = \frac{- 2 \pm \sqrt{4 (10)}}{2 \cdot 3}$

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

$x = \frac{- 2 \pm \sqrt{2^{2} \cdot 10}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{- 2 \pm 2 \sqrt{10}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 2 \pm 2 \sqrt{10}}{6}$

Simplify $\frac{- 2 \pm 2 \sqrt{10}}{6}$ .

$x = \frac{- 1 \pm \sqrt{10}}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1 \pm \sqrt{10}}{3}$

Decimal Form:

$x = 0.72075922 \dots, - 1.38742588 \dots$

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Name

Name	one billion three hundred eighty-nine million eight hundred eleven thousand two hundred fifty-nine

Interesting facts

1389811259 has 4 divisors, whose sum is 1462959240
The reverse of 1389811259 is 9521189831
Previous prime number is 19

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 47
Digital Root 2

Name

Name	one billion two hundred forty-seven million six hundred eighty-six thousand nine hundred fifteen

Interesting facts

1247686915 has 8 divisors, whose sum is 1545522048
The reverse of 1247686915 is 5196867421
Previous prime number is 31

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 49
Digital Root 4

Name

Name	one hundred ninety-seven million one hundred seven thousand two hundred thirty-eight

Interesting facts

197107238 has 16 divisors, whose sum is 308883456
The reverse of 197107238 is 832701791
Previous prime number is 83

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 38
Digital Root 2

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