Answer:
F
Explanation:
(x + 2)² + (y - 3)² = 37
intersection points with the x-axis means that their y-values are 0 !
that is the whole trick, as I am sure you experienced already with lines and y-intersects (x = 0) and x-intersects (y =0).
so, we need to solve for x, when y = 0 :
(x + 2)² + (-3)² = 37
x² + 4x + 4 + 9 = 37
x² + 4x - 24 = 0
the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-4 ± sqrt(4² - 4×1×-24))/(2×1) =
= (-4 ± sqrt(16 + 96))/2 = (-4 ± sqrt(112))/2 =
= (-4 ± sqrt(16×7))/2 = (-4 ± 4×sqrt(7))/2 =
= -2 ± 2×sqrt(7)
x1 = -2 + 2×sqrt(7)
x2 = -2 - 2×sqrt(7)
so, F is the right answer.