Final answer:
To solve the inequality (x)²d -5x-36<0, factor the quadratic equation, find the critical points, create intervals on a number line, and test the inequality in each interval. The solution is (-4, 9).
Step-by-step explanation:
To solve the inequality (x)²d -5x-36<0, we can first factor the quadratic equation:
(x)²d -5x-36 = (x+4)(x-9)
Next, we can find the critical points by setting each factor equal to 0:
x+4=0 --> x=-4
x-9=0 --> x=9
Now, we can create intervals on a number line and test the inequality in each interval:
Interval (-infinity, -4):
Pick a value less than -4, for example -5:
(-5)²d -5(-5)-36 = 25+25-36 = 14
Since 14 is greater than 0, this interval is not a solution.
Interval (-4, 9):
Pick a value between -4 and 9, for example 0:
(0)²d -5(0)-36 = -36
Since -36 is less than 0, this interval is a solution.
Interval (9, infinity):
Pick a value greater than 9, for example 10:
(10)²d -5(10)-36 = 100-50-36 = 14
Since 14 is greater than 0, this interval is not a solution.
Therefore, the solution to the inequality (x)²d -5x-36<0 is (-4, 9).