Answer :
To complete the quadratic equation that models the situation where a car travels a total of 155 miles over x hours at a speed of 12x + 32, we start with the formula for distance:
Distance=Speed×Time
Given that the speed is 12x+32 and the total distance traveled is 155 miles, we set up the equation as follows:
155=(12x+32)×x
Expanding the right side of the equation: 155=12x2+32x
Therefore, the completed quadratic equation that models the situation is: 12x2+32x−155=0
To find the solution for this quadratic equation, we can use the quadratic formula: x=2a−b±√b2−4ac
For the equation 12x2+32x−155=0: - a=12 - b=32 - c=−155
Plugging these values into the quadratic formula will give us the solutions for x.
