Solve for x 2=x^2+x

$2 = x^{2} + x$

Step 1

Rewrite the equation as $x^{2} + x = 2$ .

$x^{2} + x = 2$

Step 2

Subtract $2$ from both sides of the equation.

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

Step 3

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

$- 1, 2$

Write the factored form using these integers.

$(x - 1) (x + 2) = 0$

Step 4

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

$x - 1 = 0$

$x + 2 = 0$

Step 5

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 6

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

The final solution is all the values that make $(x - 1) (x + 2) = 0$ true.

$x = 1, - 2$

Solve for x 2=x^2+x

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