Solving quadratic equation using quadratic formula (Algebra 2)

When a student is asked to solve a quadratic equation, one of the method that can never fail to find the roots of the quadratic equation is to use the quadratic formula.

Most of the time, there are 2 solutions to a quadratic equations (even though sometimes it can be just one solutions).  So the formula to find the first solution is

x1 = [-b + sqrt(b^2 - 4ac)]/2a

x2 = [-b - sqrt(b^2 - 4ac)]/2a

The thing that students need to be aware of using the quadratic formula is to make sure that they know how to apply the formula.  In order to apply the formula, you need to change the equation to its standard form, which is

ax^2 + bx + c = 0

We will use the following equation to demonstrate how to use the quadratic formula. 

x^2 = 4 - 3x

Let's change the equation to the standard form:

x^2 + 3x - 4 = 0

In this case a = 1, b = 3, c = -4, let's apply the formula.

x1 = [-b + sqrt(b^2 - 4ac)]/2a
x1 = [-3 + sqrt(3^2 - 4*1*-4)]/2*1
x1 = [-3 + sqrt(25)]/2
x1 = [-3 + 5]/2
x1 = 1

x2 = [-b - sqrt(b^2 - 4ac)]/2a
x2 = [-3 - sqrt(3^2 - 4*1*-4)]/2*1
x2 = [-3 - sqrt(25)]/2
x2 = [-3 - 5]/2
x2 = -4

If you have any question regarding this type of problems, please feel free to reach out to me or any of the instructors in my center.

Michael Huang
Mathnasium of Glen Rock/Ridgewood
236 Rock Road
Glen Rock, NJ 07452
glenrock@mathnasium.com
Tel:  201-444-8020