Trigonometry Examples

$2 x^{2} - 20 x + 48 = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Factor $2$ out of $2 x^{2} - 20 x + 48$ .

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Step 1.1.1

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) - 20 x + 48 = 0$

Step 1.1.2

Factor $2$ out of $- 20 x$ .

$2 (x^{2}) + 2 (- 10 x) + 48 = 0$

Step 1.1.3

Factor $2$ out of $48$ .

$2 x^{2} + 2 (- 10 x) + 2 \cdot 24 = 0$

Step 1.1.4

Factor $2$ out of $2 x^{2} + 2 (- 10 x)$ .

$2 (x^{2} - 10 x) + 2 \cdot 24 = 0$

Step 1.1.5

Factor $2$ out of $2 (x^{2} - 10 x) + 2 \cdot 24$ .

$2 (x^{2} - 10 x + 24) = 0$

Step 1.2

Factor.

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Step 1.2.1

Factor $x^{2} - 10 x + 24$ using the AC method.

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Step 1.2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $24$ and whose sum is $- 10$ .

$- 6, - 4$

Step 1.2.1.2

Write the factored form using these integers.

$2 ((x - 6) (x - 4)) = 0$

Step 1.2.2

Remove unnecessary parentheses.

$2 (x - 6) (x - 4) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 6 = 0$

$x - 4 = 0$

Step 3

Set $x - 6$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Step 3.2

Add $6$ to both sides of the equation.

$x = 6$

Step 4

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 4.2

Add $4$ to both sides of the equation.

$x = 4$

Step 5

The final solution is all the values that make $2 (x - 6) (x - 4) = 0$ true.

$x = 6, 4$