Solve by Factoring x^2=x+30

$x^{2} = x + 30$

Step 1

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

Subtract $x$ from both sides of the equation.

$x^{2} - x = 30$

Subtract $30$ from both sides of the equation.

$x^{2} - x - 30 = 0$

Step 2

Factor $x^{2} - x - 30$ 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 $- 30$ and whose sum is $- 1$ .

$- 6, 5$

Write the factored form using these integers.

$(x - 6) (x + 5) = 0$

Step 3

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

$x - 6 = 0$

$x + 5 = 0$

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 $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 6

The final solution is all the values that make $(x - 6) (x + 5) = 0$ true.

$x = 6, - 5$

Solve by Factoring x^2=x+30

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