Precalculus Examples

$x (x - 14) + 48 = 0$

Step 1

Apply the distributive property.

$x \cdot x + x \cdot - 14 + 48 = 0$

Step 2

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 14 + 48 = 0$

Step 3

Move $- 14$ to the left of $x$ .

$x^{2} - 14 x + 48 = 0$

Step 4

Factor $x^{2} - 14 x + 48$ using the AC method.

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Step 4.1

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 $48$ and whose sum is $- 14$ .

$- 8, - 6$

Step 4.2

Write the factored form using these integers.

$(x - 8) (x - 6) = 0$

Step 5

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

$x - 8 = 0$

$x - 6 = 0$

Step 6

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

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Step 6.1

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Step 6.2

Add $8$ to both sides of the equation.

$x = 8$

Step 7

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

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Step 7.1

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

$x - 6 = 0$

Step 7.2

Add $6$ to both sides of the equation.

$x = 6$

Step 8

The final solution is all the values that make $(x - 8) (x - 6) = 0$ true.

$x = 8, 6$