# How do you solve # 14-5x-x^2<0#?

These are the only two possible points where the expression can change signs. Thus, there are three regions that have the same sign:

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To solve ( 14 - 5x - x^2 < 0 ):

- Rearrange the equation to set it equal to zero: ( -x^2 - 5x + 14 < 0 ).
- Factor the quadratic expression if possible.
- Find the critical points by setting the expression equal to zero.
- Use test points in each interval determined by the critical points to determine where the inequality holds true.
- Write the solution set based on the intervals where the inequality is satisfied.

Alternatively, you can use the quadratic formula to find the roots of the quadratic equation and then analyze the sign of the expression within the intervals determined by the roots.

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