Final answer:
The values of x where h(x) equals g(x) are x = -2 and x = -5, found by setting h(x) equal to g(x) and factoring the resulting quadratic equation.
Step-by-step explanation:
To find the value(s) of x for which h(x) is equal to g(x), we set the two functions equal to each other and solve for x:
h(x) = g(x)
x² + 3x + 7 = -4x - 3
To solve for x, we'll move all terms to one side:
x² + 3x + 4x + 7 + 3 = 0
x² + 7x + 10 = 0
We now have a quadratic equation. Next, we'll factor:
(x + 2)(x + 5) = 0
Setting each factor equal to zero gives us the two solutions for x:
x + 2 = 0 ⇒ x = -2
x + 5 = 0 ⇒ x = -5
So, the values of x where h(x) equals g(x) are x = -2 and x = -5.