Final answer:
The solutions to the system of equations y = x^2 + 4x + 4 and y = 5x + 10 are found by setting them equal to each other, simplifying to a quadratic equation, and factoring. The solutions are x = 3 and x = -2.
Step-by-step explanation:
To find the x values for the solutions to the system of equations:
- y = x^2 + 4x + 4
- y = 5x + 10
We set the two equations equal to each other since they both equal y:
x^2 + 4x + 4 = 5x + 10
Moving all terms to one side gives us:
x^2 + 4x - 5x + 4 - 10 = 0
This simplifies to the quadratic equation:
x^2 - x - 6 = 0
Factoring the quadratic equation, we get:
(x - 3)(x + 2) = 0
Setting each factor equal to zero gives us the x-values:
- x - 3 = 0 → x = 3
- x + 2 = 0 → x = -2
Therefore, the solutions to the system are x = 3 and x = -2.