Algebra Examples

$2 x^{2} + 6 x + 3 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 2$ , $b = 6$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (2 \cdot 3)}}{2 \cdot 2}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $6$ to the power of $2$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 2 \cdot 3}}{2 \cdot 2}$

Step 3.1.2

Multiply $- 4 \cdot 2 \cdot 3$ .

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Step 3.1.2.1

Multiply $- 4$ by $2$ .

$x = \frac{- 6 \pm \sqrt{36 - 8 \cdot 3}}{2 \cdot 2}$

Step 3.1.2.2

Multiply $- 8$ by $3$ .

$x = \frac{- 6 \pm \sqrt{36 - 24}}{2 \cdot 2}$

Step 3.1.3

Subtract $24$ from $36$ .

$x = \frac{- 6 \pm \sqrt{12}}{2 \cdot 2}$

Step 3.1.4

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 3.1.4.1

Factor $4$ out of $12$ .

$x = \frac{- 6 \pm \sqrt{4 (3)}}{2 \cdot 2}$

Step 3.1.4.2

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

$x = \frac{- 6 \pm \sqrt{2^{2} \cdot 3}}{2 \cdot 2}$

Step 3.1.5

Pull terms out from under the radical.

$x = \frac{- 6 \pm 2 \sqrt{3}}{2 \cdot 2}$

Step 3.2

Multiply $2$ by $2$ .

$x = \frac{- 6 \pm 2 \sqrt{3}}{4}$

Step 3.3

Simplify $\frac{- 6 \pm 2 \sqrt{3}}{4}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.63397459 \dots, - 2.36602540 \dots$