Pre-Algebra Examples

$x^{2} - 13 x + 42 = 0$

Step 1

Factor $x^{2} - 13 x + 42$ 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 $42$ and whose sum is $- 13$ .

$- 7, - 6$

Step 1.2

Write the factored form using these integers.

$(x - 7) (x - 6) = 0$

Step 2

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

$x - 7 = 0$

$x - 6 = 0$

Step 3

Set $x - 7$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Step 3.2

Add $7$ to both sides of the equation.

$x = 7$

Step 4

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

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Step 4.1

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

$x - 6 = 0$

Step 4.2

Add $6$ to both sides of the equation.

$x = 6$

Step 5

The final solution is all the values that make $(x - 7) (x - 6) = 0$ true.

$x = 7, 6$