Trigonometry Examples

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

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

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

Step 3

Simplify.

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Step 3.1

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

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Step 3.1.1

Multiply $- 4$ by $2$ .

$x = \frac{- k \pm \sqrt{k^{2} - 8 \cdot 3}}{2 \cdot 2}$

Step 3.1.2

Multiply $- 8$ by $3$ .

$x = \frac{- k \pm \sqrt{k^{2} - 24}}{2 \cdot 2}$

Step 3.2

Multiply $2$ by $2$ .

$x = \frac{- k \pm \sqrt{k^{2} - 24}}{4}$

Step 4

The final answer is the combination of both solutions.

$x = - \frac{k - \sqrt{k^{2} - 24}}{4}$

$x = - \frac{k + \sqrt{k^{2} - 24}}{4}$