Solve for x x(x+1)-x^2+8=0

$x (x + 1) - x^{2} + 8 = 0$

Step 1

Simplify $x (x + 1) - x^{2} + 8$ .

Simplify each term.

Apply the distributive property.

$x \cdot x + x \cdot 1 - x^{2} + 8 = 0$

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1 - x^{2} + 8 = 0$

Multiply $x$ by $1$ .

$x^{2} + x - x^{2} + 8 = 0$

Combine the opposite terms in $x^{2} + x - x^{2} + 8$ .

Subtract $x^{2}$ from $x^{2}$ .

$x + 0 + 8 = 0$

Add $x$ and $0$ .

$x + 8 = 0$

Step 2

Subtract $8$ from both sides of the equation.

$x = - 8$