Solve by Factoring x^2+3x=54

$x^{2} + 3 x = 54$

Step 1

Subtract $54$ from both sides of the equation.

$x^{2} + 3 x - 54 = 0$

Step 2

Factor $x^{2} + 3 x - 54$ 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 $- 54$ and whose sum is $3$ .

$- 6, 9$

Write the factored form using these integers.

$(x - 6) (x + 9) = 0$

Step 3

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

$x - 6 = 0$

$x + 9 = 0$

Step 4

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

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

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Step 5

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

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

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

Step 6

The final solution is all the values that make $(x - 6) (x + 9) = 0$ true.

$x = 6, - 9$

Solve by Factoring x^2+3x=54

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