Algebra Examples

$X^{2} + 3 X = 18$

Step 1

Subtract $18$ from both sides of the equation.

$X^{2} + 3 X - 18 = 0$

Step 2

Factor $X^{2} + 3 X - 18$ using the AC method.

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Step 2.1

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 $- 18$ and whose sum is $3$ .

$- 3, 6$

Step 2.2

Write the factored form using these integers.

$(X - 3) (X + 6) = 0$

Step 3

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

$X - 3 = 0$

$X + 6 = 0$

Step 4

Set $X - 3$ equal to $0$ and solve for $X$ .

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Step 4.1

Set $X - 3$ equal to $0$ .

$X - 3 = 0$

Step 4.2

Add $3$ to both sides of the equation.

$X = 3$

Step 5

Set $X + 6$ equal to $0$ and solve for $X$ .

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Step 5.1

Set $X + 6$ equal to $0$ .

$X + 6 = 0$

Step 5.2

Subtract $6$ from both sides of the equation.

$X = - 6$

Step 6

The final solution is all the values that make $(X - 3) (X + 6) = 0$ true.

$X = 3, - 6$