Calculus Examples

$f (x) = 6 x - 16$ , $f (x) = - x^{2}$

Add $- x^{2}$ to both sides of the equation.

$6 x - 16 + x^{2} = 0$

Factor $6 x - 16 + x^{2}$ using the AC method.

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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 $- 16$ and whose sum is $6$ .

$- 2, 8 = 0$

Write the factored form using these integers.

$(x - 2) (x + 8) = 0$

Set $x - 2$ equal to $0$ and solve for $x$ .

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Set the factor equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set $x + 8$ equal to $0$ and solve for $x$ .

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Set the factor equal to $0$ .

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

The solution is the result of $x - 2 = 0$ and $x + 8 = 0$ .

$x = 2, - 8$

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