Solve for x x+10=x^2+x+1

$x + 10 = x^{2} + x + 1$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} + x + 1 = x + 10$

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$x^{2} + x + 1 - x = 10$

Combine the opposite terms in $x^{2} + x + 1 - x$ .

Subtract $x$ from $x$ .

$x^{2} + 0 + 1 = 10$

Add $x^{2}$ and $0$ .

$x^{2} + 1 = 10$

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$x^{2} = 10 - 1$

Subtract $1$ from $10$ .

$x^{2} = 9$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$