Precalculus Examples

$x^{2} - 8 x - 20 = 0$

Step 1

Factor $x^{2} - 8 x - 20$ using the AC method.

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Step 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 $- 20$ and whose sum is $- 8$ .

$- 10, 2$

Step 1.2

Write the factored form using these integers.

$(x - 10) (x + 2) = 0$

Step 2

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

$x - 10 = 0$

$x + 2 = 0$

Step 3

Set $x - 10$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Step 3.2

Add $10$ to both sides of the equation.

$x = 10$

Step 4

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

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Step 4.1

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Step 4.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 5

The final solution is all the values that make $(x - 10) (x + 2) = 0$ true.

$x = 10, - 2$

Step 6