How do you solve using the completing the square method #x^2 – 8x = –11#?
My answer was meant to help rapidly. Stress can make students unable to process explanations. Now on to the explanation.
If you have an equation of the type
you know how to solve.
What if you have terms linear in x too? Well this is your lucky day.
For you know that
If you stare at this equation long enough, you see that the right hand side has a term in x, but the left hand side is a square. No x. And if it's a square, you know how to solve, right?
So all you need is to work BACKWARD. From the right hand side to the left hand side.
Let's do it.
The linear term in our equation is
This gives you
So your original equation now reads
move 16 to the other side
This is an equation of the second degree. It has two roots, since 5 is positive.
Back to x. Two solutions
And you're done :)