Question

The first step in determining the solution to the system of equations, y = –x^2 – 4x – 3 and y = 2x + 5, algebraically is to set the two equations equal as –x^2 – 4x – 3 = 2x + 5. What is the next step?

Answer 1

Answer:

The next step is to put all terms into the left side of the equation and group the like trems

Step-by-step explanation:

The first step in determining the solution to the system of equations, $y =-x^2-4x-3$ and $y = 2x + 5$, algebraically is to set the two equations equal as $-x^2-4x-3 = 2x + 5.$

The next step is to put all terms into the left side of the equation and group the like trems:

$-x^2-4x-3-2x-5=0,\\ \\-x^2+(-4x-2x)+(-3-5)=0,\\ \\-x^2-6x-8=0.$

Now you can multiply this equation by -1:

$x^2+6x+8=0$

and solve it using quadratic formula:

$x_{1,2}=\dfrac{-6\pm \sqrt{6^2-4\cdot 8\cdot 1}}{2\cdot 1}=\dfrac{-6\pm\sqrt{4}}{2}=\dfrac{-6\pm 2}{2}=-4,\ -2.$