Solving quadratics by completing the square 2

The  exercise appears under the Algebra I Math Mission. This exercise uses the completion of the square technique to solve quadratic equations with slightly more difficult answers than the first level of the exercise.

Types of Problems
There is one type of problem in this exercise:


 * 1) Complete the square and use it to solve the equation: This problem provides a quadratic equation. The student is asked to complete the square, write a particular equivalent form of the equation, and provide solution(s) to the equation.Sqbcts2-1.png

Strategies
Knowledge of the process of completing the square would ensure accuracy and efficiency on this exercise.
 * 1) To complete the square, the desired number would be the coefficient of the linear term, divided by two, and then squared.
 * 2) If the linear coefficient is b and the constant term is c, the completed form will be $$ (x+\frac{b}{2})^2=(\frac{b^2}{4}-c)$$.
 * 3) The answers on this version of the exercise can be fractions, especially in the "squared" form before applying the Square Root Property.

Real-life Applications

 * 1) Completing the square in an expression, such as this exercise, allows a general quadratic to be written in vertex form which is a form that reduces the work needed to find the vertex of a quadratic.
 * 2) Completing the square is used to prove the quadratic formula.
 * 3) Quadratics are used to model many physical situations, such as gravity.