Completing the square is a method used to solve quadratic equations.
When do this, we want a perfect square trinomial on the left side.
First get rid of the constant by subtracting 12 from both sides.
This gives us s² - 8s ___ = -12 ___.
Notice that I left room for a space.
The number that goes inside the space will be the number
that is needed to create a perfect square trinomial.
So what is that number?
Well it comes from a formula.
The number that goes in the space will be half
the coefficient of the middle term squared.
Half of -8 is -4 and if we square -4, we get +16.
So a +16 goes in each blank.
So we have s² - 8s + 16 = -12 + 16.
Now the left side factors as (s - 4)² and the right side simplifies to 4.
So we have (s - 4)² = 4.
Now get rid of the squared by square rooting both sides.
So [tex]\sqrt{(s - 4)^{2}} = \sqrt{4}[/tex].
This gives us s - 4 = ±2.
Don't forget to use plus or minus when
square rooting both sides of an equation.
So either s - 4 = 2 or s - 4 = -2.
Solving each equation from here, we get s = 2 or s = 6.
Let's write our answer inset notation.
{2, 6}.
