How do you solve the following Quadratic Inequality #x^2+2x15<0#?
The solution is
There are more than one ways to solve this inequality.
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To solve the quadratic inequality (x^2 + 2x  15 < 0):

Find the critical points by setting the quadratic expression equal to zero and solving for (x).
(x^2 + 2x  15 = 0)
Factor the quadratic expression or use the quadratic formula to find the roots.
(x^2 + 5x  3x  15 = 0)
(x(x + 5)  3(x + 5) = 0)
((x  3)(x + 5) = 0)
(x = 3) or (x = 5) 
Plot these critical points on the number line.
(\begin{array}{cccccccc}
 & 5 &  & 3 & + \ \end{array})

Choose test points within each interval formed by the critical points and evaluate the quadratic expression (x^2 + 2x  15) at these points.
Test point in (( \infty, 5)): (x = 6), (x^2 + 2x  15 = (6)^2 + 2(6)  15 = 36  12  15 = 9 > 0)
Test point in ((5, 3)): (x = 0), (x^2 + 2x  15 = (0)^2 + 2(0)  15 = 15 < 0)
Test point in ((3, +\infty)): (x = 4), (x^2 + 2x  15 = (4)^2 + 2(4)  15 = 16 + 8  15 = 9 > 0) 
Determine the sign of the quadratic expression within each interval.
In (( \infty, 5)), the expression is positive ((> 0)).
In ((5, 3)), the expression is negative ((< 0)).
In ((3, +\infty)), the expression is positive ((> 0)). 
Determine the solution to the inequality based on the signs determined in step 4.
The solution to (x^2 + 2x  15 < 0) is (x) belonging to the interval ((5, 3)).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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