Solve by Factoring x^2=x+56

$x^{2} = x + 56$

Step 1

Move all the expressions to the left side of the equation.

Subtract $x$ from both sides of the equation.

$x^{2} - x = 56$

Subtract $56$ from both sides of the equation.

$x^{2} - x - 56 = 0$

Step 2

Factor $x^{2} - x - 56$ 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 $- 56$ and whose sum is $- 1$ .

$- 8, 7$

Write the factored form using these integers.

$(x - 8) (x + 7) = 0$

Step 3

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

$x - 8 = 0$

$x + 7 = 0$

Step 4

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

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

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Step 5

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

Step 6

The final solution is all the values that make $(x - 8) (x + 7) = 0$ true.

$x = 8, - 7$

Solve by Factoring x^2=x+56

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