 completing the square subtraction. Consider the expression x squared minus 8x. We can think about this as a square of side x and a rectangle of say length x and width 8. If we cut this rectangle in half so that we have two rectangles of dimensions x by 4 and we place one of them here to take it away. We're taking away this rectangle from this square and now we place this one here to take away this other rectangle. We see here that we took away this little piece twice and that's 4 by 4 so we took away sixteen square units from there the first time and then when we since we took it away a second time now we have to add those sixteen square units. So this is a new square of dimensions x minus 4. Also this x minus 4, this square the area of that square is just 8 square minus 8x plus the sixteen square units that we subtracted. Can we use that to solve an equation such as this? Yes and this is the technique called completing the square. Let's first add negative 3 to both sides of this equation to get this. Now we know that we can complete this left hand side by adding 16 units. If we do it to one side we do it to the other. We know that this factors as x minus 4 square is equal to 13. If we now take the square roots to both sides of this equation we get that x minus 4 is equal to plus or minus the square root of 13. That is x is equal to 4 plus or minus the square root of 13. So we have that x is equal to 4 plus the square root of 13 or x is equal to 4 minus the square root of 13 and those are the two solutions to this equation which we solved by applying the technique called completing the square. Thank you.