To solve the system of equations algebraically, the next step after setting the two equations equal to each other, [tex]\(-x^2 - 4x - 3 = 2x + 5\)[/tex], is to combine like terms onto one side of the equation.
1. Set the equations equal:
[tex]\(-x^2 - 4x - 3 = 2x + 5\)[/tex].
2. Move all terms to one side:
[tex]\[
-x^2 - 4x - 3 - 2x - 5 = 0
\][/tex]
3. Combine like terms:
[tex]\[
-x^2 - 6x - 8 = 0
\][/tex]
So, combining like terms onto one side results in the quadratic equation:
[tex]\[
-x^2 - 6x - 8 = 0
\][/tex]
This completes the next step in solving the system of equations algebraically.
