Completion of Square
We will explore the steps and method by looking at 2 examples.EXAMPLE 1
Solve for x
x2 - 7x + 12 = 0
Step 1
Make sure that the number attached to x2 is 1.
In this example, it is fine….there is no problem since the co-efficient of x2 is already 1.
x2 - 7x = -12
Step 2
Take the number attached to the “x” (the co-efficient of x) and multiply it by half.
Step 3
Square this number and add it to both sides of the equation.
Step 4
The left hand side simplifies to a perfect square.
Simplify the right hand side as well.
EXAMPLE 2
Solve for x
-6x2 - 5x + 6 = 0
Make the co-efficient of x2 to be 1.
To do this, we must divide by -6 throughout.
To do this, we must divide by -6 throughout.
The following steps are the same as before:
Multiply by 1/2
Include answer on both sides.
Introduce brackets, simplify RHS.
Solve for x.
