Lesson 7

Manipulating Equations to Equal Zero

 

Quadratic equations may not always have one side equal to 0 (e.g., −6 = x2 + 5x). If you are working with a quadratic equation like this, you can manipulate the equation to get all non-zero terms on one side and 0 on the other side. Then you can use an appropriate factoring strategy to solve the equation.

 

For example, if you were asked to solve −6 = x2 + 5x, you might proceed as follows.

 

To move −6, add 6 to both sides.

 

 

You can now factor the right side of the equation.

 

 

Now you can find values for x easily.

 

So, x = −2 and x = −3 are the required solutions.

 

Self-Check 2