2x-x(x+2)=-49

Expert intro: This is a worked algebraic simplification. The goal is to distribute, combine like terms, and isolate the variable.

Detailed walkthrough

Start with

$2x-x(x+2)=-49$

Distribute the $x$:

$2x-x^2-2x=-49$

Combine like terms:

$-x^2=-49$

Divide both sides by $-1$:

$x^2=49$

Take the square root of both sides:

$x=\pm 7$

So the complete solution set is

$\boxed{x=-7,7}$

💡 Pitfall guide

A frequent mistake is to write only $x=7$ after solving $x^2=49$. A square equation has two solutions unless the problem gives a reason to exclude one of them.

🔄 Real-world variant

If the equation had been $-x^2=0$, then the only solution would be $x=0$. If it had been $x^2=49$ in a context requiring positive values only, then $x=7$ would be the only allowed answer.

🔍 Related terms

distributive property, square root, solution set