Evaluate 18=6x+x(x-13)

$18 = 6 x + x (x - 13)$

Step 1

Rewrite the equation as $6 x + x (x - 13) = 18$ .

$6 x + x (x - 13) = 18$

Step 2

Simplify $6 x + x (x - 13)$ .

Simplify each term.

Apply the distributive property.

$6 x + x \cdot x + x \cdot - 13 = 18$

Multiply $x$ by $x$ .

$6 x + x^{2} + x \cdot - 13 = 18$

Move $- 13$ to the left of $x$ .

$6 x + x^{2} - 13 x = 18$

Subtract $13 x$ from $6 x$ .

$x^{2} - 7 x = 18$

Step 3

Subtract $18$ from both sides of the equation.

$x^{2} - 7 x - 18 = 0$

Step 4

Factor $x^{2} - 7 x - 18$ using the AC method.

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 $- 18$ and whose sum is $- 7$ .

$- 9, 2$

Write the factored form using these integers.

$(x - 9) (x + 2) = 0$

Step 5

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

$x - 9 = 0$

$x + 2 = 0$

Step 6

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Step 7

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 8

The final solution is all the values that make $(x - 9) (x + 2) = 0$ true.

$x = 9, - 2$

Evaluate 18=6x+x(x-13)

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