Answer
The two consecutive odd integers are $5$ and $7$ or $-5$ and $-3$.
Work Step by Step
$$x(x+2) = x + (x+2) + 23$$ $$x^2 + 2x = 2x + 25$$ $$x^2=25$$ $$x=±5$$
If $x=5$, then:
$$x+2 = 5+2 = 7$$
If $x=-5$, then:
$$x+2 = -5+2 = -3$$
Check: $5,7$
$$x(x+2) = x + (x+2) + 23$$ $$5(7) = 5 + 7 + 23$$ $$35=35$$
Check: $-5,-3$
$$-5(-3) = -5 + (-3) + 23$$ $$15=15$$
