Answer
Explanation
Given:
[tex]-x^2-2x-3=0[/tex]
Then, we can multiply the whole expression times -1:
[tex]x^2+2x+3=0[/tex]
Next, we can find the solution for x using the General Quadratic Formula:
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where a, b and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0. Thus, considering that in our case a = 1, b = 2 and c = 3:
[tex]x_{1,2}=\frac{2\pm\sqrt{2^2-4(1)(3)}}{2(1)}[/tex][tex]x_{1,2}=\frac{2\pm\sqrt{4-12}}{2}[/tex][tex]x_{1,2}=\frac{2\pm\sqrt{-8}}{2}[/tex]
Finally, calculating the two solutions:
[tex][/tex]
