Solving quadratics by completing the square 1

The  exercise appears under the Algebra I Math Mission. This exercise uses the completion of the square technique to solve quadratic equations.

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.Sqbcts1-1.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 are usually integers.

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.