Precalculus Examples

$24 x^{4} - 4 x - 48 = 0$

Step 1

Factor $4$ out of $24 x^{4} - 4 x - 48$ .

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Step 1.1

Factor $4$ out of $24 x^{4}$ .

$4 (6 x^{4}) - 4 x - 48 = 0$

Step 1.2

Factor $4$ out of $- 4 x$ .

$4 (6 x^{4}) + 4 (- x) - 48 = 0$

Step 1.3

Factor $4$ out of $- 48$ .

$4 (6 x^{4}) + 4 (- x) + 4 (- 12) = 0$

Step 1.4

Factor $4$ out of $4 (6 x^{4}) + 4 (- x)$ .

$4 (6 x^{4} - x) + 4 (- 12) = 0$

Step 1.5

Factor $4$ out of $4 (6 x^{4} - x) + 4 (- 12)$ .

$4 (6 x^{4} - x - 12) = 0$

Step 2

Simplify $4 (6 x^{4} - x - 12)$ .

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Step 2.1

Apply the distributive property.

$4 (6 x^{4}) + 4 (- x) + 4 \cdot - 12 = 0$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $6$ by $4$ .

$24 x^{4} + 4 (- x) + 4 \cdot - 12 = 0$

Step 2.2.2

Multiply $- 1$ by $4$ .

$24 x^{4} - 4 x + 4 \cdot - 12 = 0$

Step 2.2.3

Multiply $4$ by $- 12$ .

$24 x^{4} - 4 x - 48 = 0$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 1.15937977, 1.21830529$

Step 4