Solve by Factoring x^2-x=72

$x^{2} - x = 72$

Step 1

Subtract $72$ from both sides of the equation.

$x^{2} - x - 72 = 0$

Step 2

Factor $x^{2} - x - 72$ 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 $- 72$ and whose sum is $- 1$ .

$- 9, 8$

Write the factored form using these integers.

$(x - 9) (x + 8) = 0$

Step 3

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

$x - 9 = 0$

$x + 8 = 0$

Step 4

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 5

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

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

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 6

The final solution is all the values that make $(x - 9) (x + 8) = 0$ true.

$x = 9, - 8$

Solve by Factoring x^2-x=72

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