Nonlinear equations in one variable and systems of equations in two variables SAT question

The correct answer is $-10$. Adding $y$ to both sides of the second equation in the given system yields $20x+100=y$. Substituting $20x+100$ for $y$ in the first equation in the given system yields $x^2+20x+100+7=7$. Subtracting $7$ from both sides of this equation yields $x^2+20x+100=0$. Factoring the left-hand side of this equation yields $(x+10)(x+10)=0$, or ${(x+10)}^2=0$. Taking the square root of both sides of this equation yields $x+10=0$. Subtracting $10$ from both sides of this equation yields $x=-10$. Therefore, the value of $x$ is $-10$.