Precalculus Examples

$\frac{2 x^{2} - 3 x - 4}{x - 4} = 0$

Step 1

Set the numerator equal to zero.

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

Step 2

Solve the equation for $x$ .

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Step 2.1

Use the quadratic formula to find the solutions.

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

Step 2.2

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

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

Step 2.3

Simplify.

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Step 2.3.1

Simplify the numerator.

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Step 2.3.1.1

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

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

Step 2.3.1.2

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

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Step 2.3.1.2.1

Multiply $- 4$ by $2$ .

$x = \frac{3 \pm \sqrt{9 - 8 \cdot - 4}}{2 \cdot 2}$

Step 2.3.1.2.2

Multiply $- 8$ by $- 4$ .

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

Step 2.3.1.3

Add $9$ and $32$ .

$x = \frac{3 \pm \sqrt{41}}{2 \cdot 2}$

Step 2.3.2

Multiply $2$ by $2$ .

$x = \frac{3 \pm \sqrt{41}}{4}$

Step 2.4

The final answer is the combination of both solutions.

$x = \frac{3 + \sqrt{41}}{4}, \frac{3 - \sqrt{41}}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 + \sqrt{41}}{4}, \frac{3 - \sqrt{41}}{4}$

Decimal Form:

$x = 2.35078105 \dots, - 0.85078105 \dots$