Solving quadratic equations is one of the main topics of this unit. Some quadratic equations can be solved with only one method, some can be solved with multiple methods, and some can’t be solved at all. Think about a task in your daily life that can be accomplished in a variety of ways. How do you decide the best course of action for accomplishing that task? How is this process like choosing a method for solving a quadratic equation that can be solved in multiple ways?

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?