Algebra Examples

$0 = 4 x^{2} - 3 x + 2$

Step 1

Rewrite the equation as $4 x^{2} - 3 x + 2 = 0$ .

$4 x^{2} - 3 x + 2 = 0$

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 $a = 4$ , $b = - 3$ , and $c = 2$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 4 \cdot 2}}{2 \cdot 4}$

Step 4.1.2

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

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Step 4.1.2.1

Multiply $- 4$ by $4$ .

$x = \frac{3 \pm \sqrt{9 - 16 \cdot 2}}{2 \cdot 4}$

Step 4.1.2.2

Multiply $- 16$ by $2$ .

$x = \frac{3 \pm \sqrt{9 - 32}}{2 \cdot 4}$

Step 4.1.3

Subtract $32$ from $9$ .

$x = \frac{3 \pm \sqrt{- 23}}{2 \cdot 4}$

Step 4.1.4

Rewrite $- 23$ as $- 1 (23)$ .

$x = \frac{3 \pm \sqrt{- 1 \cdot 23}}{2 \cdot 4}$

Step 4.1.5

Rewrite $\sqrt{- 1 (23)}$ as $\sqrt{- 1} \cdot \sqrt{23}$ .

$x = \frac{3 \pm \sqrt{- 1} \cdot \sqrt{23}}{2 \cdot 4}$

Step 4.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{3 \pm i \sqrt{23}}{2 \cdot 4}$

Step 4.2

Multiply $2$ by $4$ .

$x = \frac{3 \pm i \sqrt{23}}{8}$

Step 5